Continual systems of relays

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The converter of continual systems of relays (also known as the Preisach converter) is a wellknown model applicable to describe the hysteresis relationships of a wide range. This article provides a review of works devoted to the study of systems from various subject areas (physics, economics, biology), where the continual system of relays plays a key role in the formalization of hysteresis dependencies. The first section of the work is devoted to a description of the input-output correspondences of the classical converter of continual systems of relays, its main properties are established, methods for constructing the output using the formalism of the demagnetization function are described, and a generalization of the classical converter of continual system of relays to the case of vector input-output correspondences is given. Applications of the Preisach model, classified according to various natural science fields, are given in the second section. Various generalizations of the model as applied to systems containing ferromagnetic and ferroelectric materials are described there. The main attention was paid to experimental works, where the model of continual system of relays was used to analytically describe the dependences observed in experiments. Special attention in the review is paid to technical applications of the model such as energy storage devices, systems using the piezoelectric effect, models of systems with long-term memory. The review also presents the results of using the converter of continual systems of relays in biology and medicine, as well as in economics. The third part of the review describes the properties of the converter of continual system of relays in terms of its response to stochastic external influences and provides a generalization of the converter model to the case of stochasticity of the threshold numbers of its elementary components. In addition, the review contains fresh results in the field of dynamics of systems with a converter of continual system of relays: a method for identifying dynamic modes is given, based on a modification of Benettin’s algorithm for calculating Lyapunov exponents in systems with nonsmooth multivalued characteristics.

Sobre autores

M. Semenov

Voronezh State University

Autor responsável pela correspondência
Email: mkl150@mail.ru
Voronezh, Russia

S. Borzunov

Voronezh State University

Email: sborzunov@gmail.com
Voronezh, Russia

O. Kanischeva

Voronezh State University

Email: oleka_olesya@mail.ru
Voronezh, Russia

A. Proshunin

Voronezh State University

Email: alexfrauch@gmail.com
Voronezh, Russia

P. Meleshenko

Voronezh State University

Email: melechp@yandex.ru
Voronezh, Russia

Bibliografia

  1. Борзунов С. В., Семенов М. Е., Сельвесюк Н. И., Мелешенко П. А. Гистерезисные преобразователи со случайными параметрами// Мат. модел. - 2019. - 31, № 7. - С. 109-126. - DOI: 10.1134/ S0234087919070074.
  2. Борзунов С. В., Семенов М. Е., Сельвесюк Н. И., Мелешенко П. А., Соловьев А. М. Стохастическая модель гистерезисного преобразователя с доменной структурой// Мат. модел. - 2021. - 33, № 9. - С. 60-86. - doi: 10.20948/mm-2021-09-05
  3. Красносельский М. А., Покровский А. В. Системы с гистерезисом. - М.: Наука, 1983.
  4. Красносельский А. М., Покровский А. В. Диссипативность нерезонансного маятника с ферромагнитным трением// Автомат. и телемех. - 2006. - 2. - С. 57-69.
  5. Медведский А. Л., Мелешенко П. А., Нестеров В. А., Решетова О. О., Семенов М. Е., Соловьев А. М. Неустойчивые колебательные системы с гистерезисом: задачи стабилизации и управления// Изв. РАН. Теор. и сист. управл. - 2020. - 4. - С. 58-82.
  6. Abdullah N., Hasan N. The implementation of water alternating (WAG) injection to obtain optimum recovery in Cornea Field, Australia// J. Petrol. Explor. Product. Techn. - 2021. - 11. - С. 1475-1485. - doi: 10.1007/s13202-021-01103-7.
  7. Adeyemo T., Kramer I., Levy G. J., Mau Y. Salinity and sodicity can cause hysteresis in soil hydraulic conductivity// Geoderma. - 2022. - 413. - 115765.
  8. Adly A. A., Mayergoyz I. D. Accurate modeling of vector hysteresis using a superposition of Preisach-type models// IEEE Trans. Magnet. - 1997. - 33. - С. 4155-4157.
  9. Alt H. W. On the thermostat problem// Control Cybernet. - 1985. - 14. - С. 171-193.
  10. Andreev M., Suvorov A., Ruban N., Ufa R., Gusev A., Askarov A., Kievets A. S. Development and research of mathematical model of current transformer reproducing magnetic hysteresis based on Preisach theory// IET Gener. Transm. & Distrib. - 2020. - 14. - С. 2720-2730.
  11. Apushkinskaya D. E., Uraltseva N. N. Free boundaries in problems with hysteresis// Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. - 2015. - 373, № 2050. - 20140271. - doi: 10.1098/rsta.2014.0271.
  12. Apushkinskaya D. E., Uraltseva N. N. On regularity properties of solutions to the hysteresis-type problem// Interfaces and Free Bound. - 2015. - 17, № 1. - С. 93-115. - doi: 10.4171/ifb/335.
  13. Azzerboni B., Cardelli E., Della Torre E., Finocchio G. Reversible magnetization and Lorentzian function approximation// J. Appl. Phys. - 2003. - 93. - С. 6635-6637.
  14. Bagagiolo F. Dynamic programming for some optimal control problems with hysteresis// Nonlinear Differ. Equ. Appl. - 2002. - 9. - С. 149-174.
  15. Bagagiolo F. Viscosity solutions for an optimal control problem with Preisach hysteresis nonlinearities// ESAIM: Control Optim. Calc. Var. - 2004. - 10. - С. 271-294.
  16. Balanov Z., Krawcewicz W., Rachinskii D., Zhezherun A. Hopf bifurcation in symmetric networks of coupled oscillators with hysteresis// J. Dynam. Differ. Equ. - 2012. - 24. - С. 713-759.
  17. Barker J. A., Schreiber D. E., Huth B. G., Everett D. H. Magnetic hysteresis and minor loops: Models and experiments// Proc. R. Soc. London Ser. A. Math. Phys. Sci. - 1983. - 386. - С. 251-261.
  18. Baronti F., Femia N., Saletti R., Visone C., Zamboni W. Hysteresis modeling in Li-ion batteries// IEEE Trans. Magnet. - 2014. - 50, № 11. - С. 1-4.
  19. Baronti F., Femia N., Saletti R., Visone C., Zamboni W. Preisach modelling of lithium-iron-phosphate battery hysteresis// J. Energy Storage. - 2015. - 4. - С. 51-61. - doi: 10.1016/j.est.2015.09.004.
  20. Bartic A. T., Wouters D. J., Maes H. E., Rickes J. T., Waser R. M. Preisach model for the simulation of ferroelectric capacitors// J. Appl. Phys. - 2001. - 89, № 6. - С. 3420-3425.
  21. Belbas S., Mayergoyz I. Dynamic programming for systems with hysteresis// Phys. B. - 2001. - 306.- С. 200-205.
  22. Belbas S. A., Mayergoyz I. D. Optimal control of dynamical systems with Preisach hysteresis// Int. J. Non-Linear Mech. - 2002. - 37. - С. 1351-1361.
  23. Belhaq M., Bichri A., Der Hogapian J., Mahfoud J. Effect of electromagnetic actuations on the dynamics of a harmonically excited cantilever beam// Int. J. Non-Linear Mech. - 2011. - 46. - С. 828-833.
  24. Bermu´dez A., Dupr´e L., Go´mez D., Venegas P. Electromagnetic computations with Preisach hysteresis model// Finite Elem. Anal. Design. - 2017. - 126. - С. 65-74.
  25. Bermu´dez A., Gu´mez D., Venegas P. Mathematical analysis and numerical solution of models with dynamic Preisach hysteresis// J. Comput. Appl. Math. - 2020. - 367. - С. 112452.
  26. Bertotti G. Hysteresis in magnetism: for physicists, materials scientists, and engineers. - New York: Academic Press, 1998.
  27. Bertotti G., Mayergoyz I. D., Basso V., Magni A. Functional integration approach to hysteresis// Phys. Rev. E. - 1999. - 60, № 2. - С. 1428-1440.
  28. Bodale I., Stancu A. Reversible and irreversible processes in drying and wetting of soil// Materials. - 2020. - 13, № 1. - С. 135.
  29. Bombara D., Fowzer S., Zhang J. Compliant, large-strain, and self-sensing twisted string actuators// Soft Robotics. - 2022. - 9. - С. 72-88.
  30. Borzunov S. V., Semenov M. E., Sel’vesyuk N. I., Meleshenko P. A. Generalized play-operator under stochastic perturbations: an analytic approach// J. Vibr. Engrg. Techn. - 2021. - 9. - С. 355-365. - doi: 10.1007/s42417-020-00234-1
  31. Botkin N. D., Brokate M., El Behi-Gornostaeva E. G. One-phase flow in porous media with hysteresis// Phys. B. Cond. Matt. - 2016. - 486. - С. 183-186.
  32. Brokate M. On a characterization of the Preisach model for hysteresis// Rend. Semin. Mat. Univ. Padova. - 1990. - 83. - С. 153-163.
  33. Brokate M., Friedman A. Optimal design for heat conduction problems with hysteresis// SIAM J. Control Optim. - 1989. - 27, № 4. - С. 697-717. - doi: 10.1137/032703.
  34. Brokate M., Krejˇc´ı P. Optimal control of ODE systems involving a rate independent variational inequality// Discrete Contin. Dyn. Syst. Ser. B. - 2013. - 18, № 2. - С. 331-348.
  35. Brokate M., Pokrovskii A., Rachinskii D., Rasskazov O. Differential equations with hysteresis via a canonical example// В сб.: «The Science of Hysteresis. Vol. I. Mathematical Modeling and Applications». - Amsterdam: Academic Press, 2006. - С. 125-291. - doi: 10.1016/B978-012480874-4/50005-1.
  36. Brokate M., Sprekels J. Hysteresis and phase transition. - New York: Springer, 1996.
  37. Cacciola P., Calio` I., Fiorini N., Occhipinti G., Spina D., Tombari A. Seismic response of nonlinear soil-structure interaction systems through the Preisach formalism: the Messina Bell Tower case study// Bull. Earthquake Engrg. - 2022. - 20. - С. 3485-3514.
  38. Cacciola P., Tombari A. Steady state harmonic response of nonlinear soil-structure interaction problems through the Preisach formalism// Soil Dynam. Earthquake Engrg. - 2021. - 144. - С. 106669.
  39. Carboni B., Lacarbonara W. Nonlinear dynamic characterization of a new hysteretic device: experiments and computations// Nonlinear Dynam. - 2016. - 83. - С. 23-39.
  40. Carboni B., Lacarbonara W., Brewick P., Masri S. Dynamical response identification of a class of nonlinear hysteretic systems// J. Intel. Mater. Syst. Struct. - 2018. - 29, № 13. - С. 2795-2810.
  41. Charalampakis A. E. The response and dissipated energy of Bouc-Wen hysteretic model revisited// Archive Appl. Mech. - 2015. - 85. - С. 1209-1223.
  42. Chatterjee S., Kumar S., Gaidhane A., Dabhi C. K., Chauhan Y. S., Amrouch H. Ferroelectric FDSOI FET modeling for memory and logic applications// Solid-State Electron. - 2023. - 200. - С. 108554.
  43. Chen B., Timoshin S. Optimal control of a population dynamics model with hysteresis// Acta Math. Sci. - 2022. - 42B(1). - С. 283-298.
  44. Chladn´a Z., Kopfova´ J., Rachinskii D., Rouf S. C. Global dynamics of SIR model with switched transmission rate// J. Math. Biol. - 2020. - 80. - С. 1209-1233.
  45. Chojecki P., Walters G., Forrester Z., Nishida T. Preisach modeling of imprint on hafnium zirconium oxide ferroelectric capacitors// J. Appl. Phys. - 2021. - 130. - С. 094102.
  46. Colli P., Grasselli M., Sprekels J. Automatic control via thermostats of a hyperbolic Stefan problem with memory// Appl. Math. Optim. - 1999. - 39. - С. 229-255. - doi: 10.1007/s002459900105.
  47. Cottone F., Vocca H., Gammaitoni L. Nonlinear energy harvesting// Phys. Rev. Lett. - 2009. - 102.- С. 080601.
  48. Cross R. Unemployment: natural rate epicycles or hysteresis?// Eur. J. Econom. Econom. Polic. Intervent. - 2014. - 11, № 2. - С. 136-148.
  49. Cross R., Krasnosel’skii A. M., Pokrovskii A. V. A time-dependent Preisach model// Phys. B. Cond. Matt. - 2001. - 306, № 1. - С. 206-210.
  50. Cross R., McNamara H., Pokrovskii A., Rachinskii D. A new paradigm for modelling hysteresis in macroeconomic flows// Phys. B. Cond. Matt. - 2008. - 403, № 2-3. - С. 231-236.
  51. Curran M., Gurevich P., Tikhomirov S. Recent advances in reaction-diffusion equations with non-ideal relays// В сб.: «Control of Self-Organizing Nonlinear Systems. Understanding Complex Systems». - Springer, 2016. - doi: 10.1007/978-3-319-28028-8_11.
  52. Dafri M., Ladjimi A., Mendaci S., Babouri A. Phenomenological model of the temperature dependence of hysteresis based on the Preisach model// J. Superconduct. Nov. Magnet. - 2021. - 34. - С. 1453-1458.
  53. Daqaq M. F., Masana R., Erturk A., Dane Q. D. On the role of nonlinearities in vibratory energy harvesting: A critical review and discussion// Appl. Mech. Rev. - 2013. - 66. - С. 040801.
  54. Darbenas Z., Van der Hout R., Oliver M. Long-time asymptotics of solutions to the Keller-Rubinow model for Liesegang rings in the fast reaction limit// Ann. Inst. H. Poincar´e Anal. Non Lin´eaire. - 2022. - 39, № 6. - С. 1413-1458. - doi: 10.4171/aihpc/34.
  55. Darbenas Z., Van der Hout R., Oliver M. Conditional uniqueness of solutions to the Keller-Rubinow model for Liesegang rings in the fast reaction limit// J. Differ. Equ. - 2023. - 347. - С. 212-245. - doi: 10.1016/j.jde.2022.11.038.
  56. Das S. G., Krug J., Mungan M. Driven disordered systems approach to biological evolution in changing environments// Phys. Rev. X. - 2022. - 12. - С. 031040.
  57. Detmann B., Krejˇc´ı P. A multicomponent flow model in deformable porous media// Math. Methods Appl. Sci. - 2019. - 42. - С. 1894-1906.
  58. Dho J., Leung C. W., Blamire M. G. Universal time relaxation behavior of the exchange bias in ferromagnetic/antiferromagnetic bilayers// J. Appl. Phys. - 2006. - 99. - С. 033910.
  59. Di Matteo A. Response of nonlinear oscillators with fractional derivative elements under evolutionary stochastic excitations: A Path Integral approach based on Laplace’s method of integration// Probab. Engrg. Mech. - 2023. - 71. - С. 103402.
  60. Dupre L. R., Van Keer R., Melkebeek J. A. A. Identification of the relation between the material parameters in the Preisach model and in the Jiles-Atherton hysteresis model// J. Appl. Phys. - 1999. - 85. - С. 4376- 4378.
  61. Eleuteri M., Ipocoana E., Kopfova´ J., Krejˇc´ı P. Periodic solutions of a hysteresis model for breathing// ESAIM Math. Model. Numer. Anal. - 2020. - 54, № 1. - С. 255-271.
  62. Enab K., Emami-Meybodi H. Effects of diffusion, adsorption, and hysteresis on huff-n-puff performance in ultratight reservoirs with different fluid types and injection gases// Energies. - 2021. - 14. - С. 7379. - doi: 10.3390/en14217379.
  63. Evans L. C., Portilheiro M. Irreversibility and hysteresis for a forward-backward diffusion equation// Math. Models Methods Appl. Sci. - 2004. - 14. - 1599-1620. - doi: 10.1142/S0218202504003763.
  64. Everett D. H. A general approach to hysteresis. Part 3. - A formal treatment of the independent domain model of hysteresis// Trans. Faraday Soc. - 1954. - 50. - С. 1077-1096.
  65. Everett D. H., Whitton W. I. A general approach to hysteresis// Trans. Faraday Soc. - 1952. - 48.- С. 749-757.
  66. Flynn D., Zhezherun A., Pokrovskii A., O’Kane J. P. Modeling discontinuous flow through porous media using ODEs with Preisach operator// Phys. B. - 2008. - 403. - С. 440-442.
  67. Franzitta V., Viola A., Trapanese M. Description of hysteresis in Lithium battery by classical Preisach model// Adv. Mater. Res. - 2012. - 622-623. - С. 1099-1103.
  68. Friedman A., Jiang L. S. Periodic solutions for a thermostat control problem// Commun. Part. Differ. Equ. - 1988. - 13, № 5. - С. 515-550. - doi: 10.1080/03605308808820551.
  69. Friedman G., Gurevich P., McCarthy S., Rachinskii D. Switching behaviour of two-phenotype bacteria in varying environment// J. Phys. Conf. Ser. - 2015. - 585. - С. 012012.
  70. Gavioli C., Krejˇc´ı P. Control and controllability of PDEs with hysteresis// Appl. Math. Optim. - 2021. - 84. - С. 829-847.
  71. Gavioli C., Krejˇc´ı P. Phase transitions in porous media// NoDEA Nonlinear Differ. Equ. Appl. - 2022. - 29. - С. 1-55.
  72. Ghouli Z., Belhaq M. Energy harvesting in a delay-induced parametric van der Pol-Duffing oscillator// Eur. Phys. J. Spec. Top. - 2021. - 230. - С. 3591-3598.
  73. Ghouli Z., Litak G. Effect of high-frequency excitation on a bistable energy harvesting system// J. Vibr. Engrg. Techn. - 2023. - 11. - С. 99-106.
  74. Glashoff K., Sprekels J. An application of Glicksberg’s theorem to set-valued integral equations arising in the theory of thermostats// SIAM J. Math. Anal. - 1981. - 12, № 3. - С. 477-486. - doi: 10.1137/0512041.
  75. Grech C., Buzio M., Pentella M., Sammut N. Dynamic ferromagnetic hysteresis modelling using a Preisach-recurrent neural network model// Materials. - 2020. - 13. - С. 2561.
  76. Guan R., Kopfova´ J., Rachinskii D. Global stability of SIR model with heterogeneous transmission rate modeled by the Preisach operator// ArXiv. - 2022. - 2201.05722.
  77. Gu¨nter R. Hysteresis-induced long-time tails// Phys. Rev. Lett. - 2008. - 100. - С. 240602.
  78. Gu¨nter R. Spectral properties of the Preisach hysteresis model with random input. I. General results// Phys. Rev. E. - 2008. - 77. - С. 061133.
  79. Gu¨nter R. Spectral properties of the Preisach hysteresis model with random input. II. Universality classes for symmetric elementary loops// Phys. Rev. E. - 2008. - 77. - С. 061134.
  80. Gurevich P. Periodic solutions of parabolic problems with hysteresis on the boundary// Discrete Cont. Dynam. Syst. A. - 2011. - 29, № 3. - С. 1041-1083. - doi: 10.3934/dcds.2011.29.1041.
  81. Gurevich P., Ja¨ger W. Parabolic problems with the Preisach hysteresis operator in boundary conditions// J. Differ. Equ. - 2009. - 47, № 11. - С. 2966-3010. - doi: 10.1016/j.jde.2009.07.033.
  82. Gurevich P., Ja¨ger W., Skubachevskii A. On periodicity of solutions for thermocontrol problems with hysteresis-type switches// SIAM J. Math. Anal. - 2009. - 41, № 2. - С. 733-752. - doi: 10.1137/080718905.
  83. Gurevich P., Rachinskii D. Asymptotics of sign-changing patterns in hysteretic systems with diffusive thresholds// Asymptot. Anal. - 2016. - 96. - С. 1-22.
  84. Gurevich P., Shamin R., Tikhomirov S. Reaction-diffusion equations with spatially distributed hysteresis// SIAM J. Math. Anal. - 2013. - 45, № 3. - С. 1328-1355. - doi: 10.1137/120879889.
  85. Gurevich P., Tikhomirov S. Symmetric periodic solutions of parabolic problems with discontinuous hysteresis// J. Dynam. Differ. Equ. - 2011. - 23. - С. 923-960. - doi: 10.1007/s10884-011-9227-0.
  86. Gurevich P., Tikhomirov S. Uniqueness of transverse solutions for reaction-diffusion equations with spatially distributed hysteresis// Nonlinear Anal. - 2012. - 75. - С. 6610-6619. - doi: 10.1016/j.na.2012.08.003.
  87. Gurevich P., Tikhomirov S. Systems of reaction-diffusion equations with spatially distributed hysteresis// Math. Bohem. - 2014. - 139. - С. 239-257. - doi: 10.21136/MB.2014.143852.
  88. Gurevich P., Tikhomirov S. Rattling in spatially discrete diffusion equations with hysteresis// Multiscale Model. Simul. - 2017. - 15, № 3. - С. 1176-1197. - doi: 10.1137/16M106039X.
  89. Gurevich P., Tikhomirov S. Spatially discrete reaction-diffusion equations with discontinuous hysteresis// Ann. Inst. H. Poincar´e Anal. Non Lin´eaire. - 2018. - 35, № 4. - С. 1041-1077. - doi: 10.1016/j.anihpc.2017.09.006.
  90. Hanyga A., Seredyn´ska M. A dynamic model of capillary hysteresis in immiscible fluid displacement// Transp. Porous Media. - 2005. - 59, № 3. - С. 249-265. - doi: 10.1007/s11242-004-2555-3.
  91. Harb A. Energy harvesting: State-of-the-art// Renewable Energy. - 2011. - 36, № 10. - С. 2641-2654.
  92. Hoffmann K.-H., Sprekels J., Visintin A. Identification of hysteresis loops// J. Comput. Phys. - 1988. - 78, № 1. - С. 215-230.
  93. Hoppensteadt F. C., Ja¨ger W. Pattern formation by bacteria// Lect. Notes Biomath. - 1980. - 38.- С. 68-81. - doi: 10.1007/978-3-642-61850-5_7.
  94. Hoppensteadt F. C., Ja¨ger W., Po¨ppe C. A hysteresis model for bacterial growth patterns// Lect. Notes Biomath. - 1984. - 55. - С. 123-134. - doi: 10.1007/978-3-642-45589-6_11.
  95. Hu H., Ben Mrad R. On the classical Preisach model for hysteresis in piezoceramic actuators// Mechatronics. - 2003. - 13. - С. 85-94.
  96. Ikhouane F. A survey of the hysteretic Duhem model// Arch. Comput. Methods Engrg. - 2018. - 25.- С. 965-1002.
  97. Ikhouane F., Man˜osa V., Pujol G. Minor loops of the Dahl and LuGre models// Appl. Math. Model. - 2020. - 77. - С. 1679-1690.
  98. Ikhouane F., Rodellar J. On the hysteretic Bouc-Wen model// Nonlinear Dynam. - 2005. - 42. - С. 63- 78.
  99. Il’in A. M., Markov B. A. Nonlinear diffusion equation and Liesegang rings// Dokl. Math. - 2011. - 440.- С. 164-167. - doi: 10.1134/S1064562411060093.
  100. Ipocoana E., Krejˇc´ı P. A model for assisted periodic breathing with degenerate permeability// Nonlinear Anal. Real World Appl. - 2024. - 75. - С. 103980.
  101. Iyer R. V., Shirley M. E. Hysteresis parameter identification with limited experimental data// IEEE Trans. Magnet. - 2004. - 40. - С. 3227-3239.
  102. Iyer R. V., Tan X., Krishnaprasad P. S. Approximate inversion of the Preisach hysteresis operator with application to control of smart actuators// IEEE Trans. Autom. Control. - 2005. - 50. - С. 798-810.
  103. Janaideh M. A., Naldi R., Marconi L., Krejˇc´ı P. A hybrid model for the play hysteresis operator// Phys. B. Cond. Matt. - 2013. - 430. - С. 95-98.
  104. Jiles D. C., Atherton D. L. Theory of ferromagnetic hysteresis// J. Appl. Phys. - 1984. - 55. - С. 2115- 2120.
  105. Jules T., Reid A., Daniels K. E., Mungan M., Lechenault F. Delicate memory structure of origami switches// Phys. Rev. Res. - 2022. - 4. - С. 013128.
  106. Kalma´r-Nagy T., Amann A., Kim D., Rachinskii D. The Devil is in the details: Spectrum and eigenvalue distribution of the discrete Preisach memory model// Commun. Nonlinear Sci. Numer. Simul. - 2019. - 77. - С. 1-17.
  107. Kalma´r-Nagy T., Shekhawat A. Nonlinear dynamics of oscillators with bilinear hysteresis and sinusoidal excitation// Phys. D. Nonlinear Phenom. - 2009. - 238. - С. 1768-1786.
  108. Kamachkin A. M., Potapov D. K., Yevstafyeva V. V. Dynamics of relay systems with hysteresis and harmonic perturbation// Eurasian Math. J. - 2024. - 15, № 2. - С. 48-60. - doi: 10.32523/2077-98792024-15-2-48-60.
  109. Kamenskii M., Makarenkov O. On the response of autonomous sweeping processes to periodic perturbations// Set-Valued Var. Anal. - 2016. - 24. - С. 551-563. - doi: 10.1007/s11228-015-0348-1.
  110. Kamenskii M., Makarenkov O., Wadippuli L. N. A continuation principle for periodic BV-continuous state-dependent sweeping processes// SIAM J. Math. Anal. - 2020. - 52, № 6. - С. 5598-5626. - doi: 10.1137/19M1248613.
  111. Kamenskii M. I., Obukhovskii V. V., Petrosyan G. G. On Almost Periodic Trajectories of Control Systems with Feedback in the Form of Sweeping Processes// Math. Notes. - 2023. - 114. - С. 85-91. - doi: 10.1134/S0001434623070088.
  112. Kermack W. O., McKendrick A. G. A contribution to the mathematical theory of epidemics// Proc. R. Soc. London Ser. A. Math. Phys. Eng. Sci. - 1927. - 115. - С. 700-721.
  113. Konda R., Zhang J. Hysteresis with lonely stroke in artificial muscles: Characterization, modeling, and inverse compensation// Mech. Syst. Signal Proces. - 2022. - 164. - С. 108240.
  114. Kopfova´ J., Kopf T. Differential equations, hysteresis, and time delay// Z. Angew. Math. Phys. - 2002. - 53, № 4. - С. 676-691. - doi: 10.1007/s00033-002-8176-1.
  115. Kopfova´ J., Na´bˇelkova´ P., Rachinskii D., Rouf S. C. Dynamics of SIR model with vaccination and heterogeneous behavioral response of individuals modeled by the Preisach operator// J. Math. Biol. - 2021. - 83. - С. 1-34.
  116. Kramer I., Bayer Y., Adeyemo T., Mau Y. Hysteresis in soil hydraulic conductivity as driven by salinity and sodicity - a modeling framework// Hydrol. Earth Syst. Sci. - 2021. - 25. - С. 1993-2008.
  117. Krejˇc´ı P. Resonance in Preisach systems// Appl. Math. - 2000. - 45. - С. 439-468.
  118. Krejˇc´ı P. Hysteresis in singularly perturbed problems// В сб.: «Singular Perturbations and Hysteresis». - SIAM, 2005. - С. 73-100. - doi: 10.1137/1.9780898717860.ch3.
  119. Krejˇc´ı P. A higher order energy bound in a singular Preisach circuit// Phys. B. Cond. Matt. - 2008. - 403. - С. 297-300.
  120. Krejˇc´ı P. Optimal control of ODE systems involving a rate independent variational inequality// Discrete Contin. Dyn. Syst. Ser. S. - 2013. - 6. - С. 101-119.
  121. Krejˇc´ı P., Monteiro G. A. Inverse parameter-dependent Preisach operator in thermo-piezoelectricity modeling// Discrete Contin. Dyn. Syst. Ser. B. - 2019. - 24, № 7. - С. 3051-3066.
  122. Krejˇc´ı P., O’Kane J. P., Pokrovskii A., Rachinskii D. Properties of solutions to a class of differential models incorporating Preisach hysteresis operator// Phys. D. Nonlinear Phenom. - 2012. - 241, № 22. - С. 2010-2028. doi: 10.1016/j.physd.2011.05.005
  123. Krejˇc´ı P., Petrov A. A contact problem for a piezoelectric actuator on an elasto-plastic obstacle// Fixed Point Theory Algorithms Sci. Engrg. - 2022. - 2022. - С. 1-12.
  124. Krejˇc´ı P., Rocca E., Sprekels J. Unsaturated deformable porous media flow with thermal phase transition// Math. Models Methods Appl. Sci. - 2017. - 27. - С. 2675-2710.
  125. Kuhnen K., Krejci P. Compensation of complex hysteresis and creep effects in piezoelectrically actuated systems - A new Preisach modeling approach// IEEE Trans. Autom. Control. - 2009. - 54. - С. 537-550.
  126. Lacarbonara W., Vestroni F. Nonclassical responses of oscillators with hysteresis/ Nonlinear Dynam. - 2003. - 32. - С. 235-258.
  127. Lelkes J., Kalma´r-Nagy T. Analysis of a mass-spring-relay system with periodic forcing// Nonlinear Dynam. - 2021. - 106. - С. 21-44.
  128. Li J., Huang H., Morita T. Stepping piezoelectric actuators with large working stroke for nano-positioning systems: A review// Sensors Actuators A. Phys. - 2019. - 292. - С. 39-51.
  129. Li Y., Zhou S., Litak G. Robust design optimization of a nonlinear monostable energy harvester with uncertainties// Meccanica. - 2020. - 55. - С. 1753-1762.
  130. Li Y., Zhu J., Li Y., Zhu L. A hybrid Jiles-Atherton and Preisach model of dynamic magnetic hysteresis based on backpropagation neural networks// J. Magnetism Magnet. Mater. - 2022. - 544. - С. 168655.
  131. Litak G., Margielewicz J., Ga˛ska D., Rysak A., Trigona C. On theoretical and numerical aspects of bifurcations and hysteresis effects in kinetic energy harvesters// Sensors. - 2022. - 22. - С. 381.
  132. Liu V. T., Wing H. Y. Classical Preisach model based on polynomial approximation and applied to micropiezoelectric actuators// Symmetry. - 2022. - 14. - С. 1008.
  133. Lu Q., Gang T., Hao G., Chen L. Compound optimal control of harmonic drive considering hysteresis characteristic// Mech. Sci. - 2019. - 10. - С. 383-391.
  134. Lygas K., Wolszczak P., Litak G., Sta˛czek P. Complex response of an oscillating vertical cantilever with clearance// Meccanica. - 2019. - 54. - С. 1689-1702.
  135. Mayergoyz I. D. Mathematical models of hysteresis// Phys. Rev. Lett. - 1986. - 56, № 15. - С. 1518-1521.
  136. Mayergoyz I. D. Dynamic Preisach models of hysteresis// IEEE Trans. Magnet. - 1998. - 24. - С. 2925- 2927.
  137. Mayergoyz I. Mathematical models of hysteresis and their applications. - Elsevier, 2003.
  138. Mayergoyz I. D., Adly A. A., Huang M. W., Krafft C. Experimental testing of vector Preisach models for superconducting hysteresis// IEEE Trans. Magnet. - 2000. - 36. - С. 3505-3507.
  139. Mayergoyz I., Dimian M. Analysis of spectral noise density of hysteretic systems driven by stochastic processes// J. Appl. Phys. - 2003. - 93, № 10. - С. 6826-6828.
  140. Mayergoyz I. D., Dimian M. Stochastic aspects of hysteresis// J. Phys. Conf. Ser. - 2005. - 22. - С. 139- 147.
  141. Mayergoyz I. D., Friedman G. Generalized Preisach model of hysteresis// IEEE Trans. Magnet. - 1988. - 24. - С. 212-217.
  142. Mayergoyz I. D., Friedman G., Salling C. Comparison of the classical and generalized Preisach hysteresis models with experiments// IEEE Trans. Magnet. - 1989. - 25. - С. 3925-3927.
  143. Mayergoyz I. D., Korman C. E. Preisach based storage devices and global optimizers// Math. Model. Nat. Phenom. - 2020. - 15. - С. 20.
  144. McCarthy S., Rachinskii D. Dynamics of systems with Preisach memory near equilibria// Math. Bohem. - 2014. - 139, № 1. - С. 39-73. - URL: http://dml.cz/dmlcz/143636.
  145. Mielke A. Evolution of rate-independent systems// В сб.: «Handbook of Differential Equations: Evolutionary Equations. Vol. II», Amsterdam: Elsevier/North-Holland, 2005. - С. 461-559. - doi: 10.1016/S1874-5717(06)80009-5.
  146. Moreau J. J. Rafle par un convexe variable (premi`ere partie)// Trav. S´emin. Anal. Conv. - 1971. - 1, № 15. - С. 1-43.
  147. Moreau J. J. Rafle par un convexe variable (deuxi`eme partie)// Trav. S´emin. Anal. Conv. - 1972. - 2, № 3. - С. 1-36.
  148. Moreau J. J. Evolution problem associated with a moving convex set in a Hilbert spaces// J. Differ. Equ. - 1977. - 26, № 3. - С. 347-374. - doi: 10.1016/0022-0396(77)90085-7.
  149. Mortell M. P., O’Malley R. E., Pokrovskii A., Sobolev V. Singular perturbations and hysteresis. - Philadelphia: SIAM, 2005.
  150. Mu¨nch C. Optimal control of reaction-diffusion systems with hysteresis// ESAIM: Control Optim. Calc. Var. - 2018. - 24, № 4. - С. 1453-1488.
  151. N´eel L. Th´eorie des lois d’aimantation de Lord Rayleigh: I. Les d´eplacements d’une paroi isol´ee// Cahiers de Physique. - 1942. - 12. - С. 1-20.
  152. O’Ceallaigh S., Pimenov A., Pokrovskii A., Rachinskii D., Zhezherun A. Algorithm for linear stability analysis in systems with Preisach hysteresis// Phys. B. Cond. Matt. - 2008. - 403. - С. 305-307.
  153. Ortiz-Lopez J., Luty F. Optical studies of thermal cycling and hysteresis effects in elastic order-disorder phase transformations. I. Pure alkali-metal cyanide crystals// Phys. Rev. B. - 1988. - 37, № 10. - С. 5452-5460.
  154. P´al L. Stochastic model of hysteresis// Phys. Rev. E. - 2000. - 61, № 4. - С. 3490-3500.
  155. Pasquale M., Basso V., Bertotti G., Jiles D. C., Bi Y. Domain-wall motion in random potential and hysteresis modeling// J. Appl. Phys. - 1998. - 83. - С. 6497-6499.
  156. Pei J. S., Carboni B., Lacarbonara W. Mem-models as building blocks for simulation and identification of hysteretic systems// Nonlinear Dynam. - 2020. - 100, № 2. - С. 973-998. - doi: 10.1007/s11071-02005542-5.
  157. Pimenov A., Kelly T. C., Korobeinikov A., O’Callaghan M. J., Pokrovskii A. Systems with hysteresis in mathematical biology via a canonical example// В сб.: «Mathematical Modeling, Clustering Algorithms and Applications». - Nova Sci. Publ., 2012. - С. 34.
  158. Pimenov A., Kelly T. C., Korobeinikov A., O’Callaghan M. J., Pokrovskii A. V., Rachinskii D. Memory effects in population dynamics: spread of infectious disease as a case study// Math. Model. Nat. Phenom. - 2012. - 7. - С. 204-226.
  159. Pimenov A., Kelly T. C., Korobeinikov A., O’Callaghan M. J., Rachinskii D. Memory and adaptive behavior in population dynamics: anti-predator behavior as a case study// J. Math. Biol. - 2017. - 74, № 6. - С. 1533-1559.
  160. Pimenov A., Rachinskii D. Linear stability analysis of systems with Preisach memory// Discrete Contin. Dyn. Syst. Ser. B. - 2009. - 11, № 4. - С. 997-1018. - doi: 10.3934/dcdsb.2009.11.997
  161. Pokrovskii A., Sobolev V. A naive view of time relaxation and hysteresis// В сб.: Singular Perturbations and Hysteresis. - SIAM, 2005. - С. 1-59.
  162. Preisach F. U¨ ber die magnetische Nachwirkung// Z. Phys. - 1935. - 94. - С. 277-302.
  163. Preisach F. On the magnetic aftereffect// IEEE Trans. Magnet. - 2017. - 53. - С. 0700111.
  164. Pru¨ss J. Periodic solutions of the thermostat problem// В сб.: «Differential Equations in Banach Spaces», Proc. Conf., Bologna, July 2-5, 1985. - Springer Berlin Heidelberg, 2006. - С. 216-226.
  165. Rachinskii D. Realization of arbitrary hysteresis by a low-dimensional gradient flow// Discrete Contin. Dyn. Syst. Ser. B. - 2016. - 21, № 1. - С. 227-243.
  166. Rachinskii D., Rouf S. Dynamics of SIR model with heterogeneous response to intervention policy// Theor. Popul. Biol. - 2022. - 146. - С. 71-85.
  167. Radons G., Zienert A. Nonlinear dynamics of complex hysteretic systems: Oscillator in a magnetic field// Eur. Phys. J. Spec. Topics. - 2013. - 222. - С. 1675-1684.
  168. Ramesh A., Jiles D. C., Roderick J. M. A model of anisotropic anhysteretic magnetization// IEEE Trans. Magnet. - 1996. - 32. - С. 4234-4236.
  169. Renno J. M., Daqaq M. F., Inman D. J. On the optimal energy harvesting from a vibration source// J. Sound Vibr. - 2009. - 320, № 1-2. - С. 386-405.
  170. Restorff J. B., Savage H. T., Clark A. E., Wun-Fogle M. Preisach modeling of hysteresis in Terfenol// J. Appl. Phys. - 1990. - 67. - С. 5016-5018.
  171. Robert G., Damjanovic D., Setter N. Preisach modeling of ferroelectric pinched loops// Appl. Phys. Lett. - 2000. - 77, № 26. - С. 4413-4415.
  172. Roussel R., Edelen A., Ratner D., Dubey K., Gonzalez-Aguilera J. P., Kim Y. K., Kuklev N. Differentiable Preisach modeling for characterization and optimization of particle accelerator systems with hysteresis// Phys. Rev. Lett. - 2022. - 128. - С. 204801.
  173. Ruderman M., Bertram T. Identification of soft magnetic B-H characteristics using discrete dynamic Preisach model and single measured hysteresis loop// IEEE Trans. Magnet. - 2012. - 48. - С. 1281-1284.
  174. Scalerandi M., Nobili M., Griffa M., Gliozzi A. S., Bosia F. Preisach-Mayergoyz approach to fatigueinduced irreversibility// Phys. Rev. B. - 2006. - 73. - С. 092103.
  175. Schubert S., Radons G. Preisach models of hysteresis driven by Markovian input processes// Phys. Rev. E. - 2017. - 96. - С. 022117.
  176. Schweizer B. Hysteresis in porous media: Modelling and analysis// Interfaces Free Bound. - 2017. - 19.- С. 417-447.
  177. Semenov M. E., Borzunov S. V., Meleshenko P. A. A new way to compute the Lyapunov characteristic exponents for non-smooth and discontinues dynamical systems// Nonlinear Dynam. - 2022. - 109.- С. 1805-1821. - doi: 10.1007/s11071-022-07492-6.
  178. Semenov M. E., Borzunov S. V., Meleshenko P. A., Lapin A. V. A model of optimal production planning based on the hysteretic demand curve// Mathematics. - 2022. - 10, № 18. - С. 3262. - DOI: 10.3390/ math10183262
  179. Semenov M. E., Meleshenko P. A., Borzunov S. V., Reshetova O. O., Barsukov A. I. A simple model of the energy harvester within a linear and hysteresis approach// Micromachines. - 2023. - 14. - С. 310. - doi: 10.3390/mi14020310
  180. Semenov M. E., Reshetova O. O., Borzunov S. V., Meleshenko P. A. Self-oscillations in a system with hysteresis: the small parameter approach// Eur. Phys. J. Spec. Topics. - 2021. - 230. - С. 3565-3571. - doi: 10.1140/epjs/s11734-021-00237-3.
  181. Semenov M. E., Reshetova O. O., Tolkachev A. V., Solovyov A. M., Meleshenko P. A. Oscillations under hysteretic conditions: From simple oscillator to discrete sine-Gordon model// В сб.: «Topics in Nonlinear Mechanics and Physics»ю - Singapore: Springer, 2019. - С. 229-254. - doi: 10.1007/978-981-13-94638_12.
  182. Semenov M. E., Solovyov A. M., Meleshenko P. A. Stabilization of coupled inverted pendula: From discrete to continuous case// J. Vibr. Control. - 2021. - 27, № 1-2. - С. 43-56. - doi: 10.1177/1077546320923436
  183. Semenov M. E., Solovyov A. M., Meleshenko P. A., Balthazar J. M. Nonlinear damping: from viscous to hysteretic dampers// В сб.: «Recent Trends in Applied Nonlinear Mechanics and Physics: Selected Papers from CSNDD 2016». - Cham: Springer, 2017. - С. 259-275. - doi: 10.1007/978-3-319-63937-6_15.
  184. Semenov M. E., Solovyov A. M., Meleshenko P. A., Reshetova O. O. Efficiency of hysteretic damper in oscillating systems// Math. Model. Nat. Phenom. - 2020. - 15. - С. 43. - doi: 10.1051/mmnp/2019053
  185. Spanos P. D., Cacciola P., Redhorse J. Random vibration of SMA systems via Preisach formalism// Nonlinear Dynam. - 2004. - 36. - С. 405-419.
  186. Spanos P. D., Matteo A., Di Pirrotta A. Steady-state dynamic response of various hysteretic systems endowed with fractional derivative elements// Nonlinear Dynam. - 2019. - 98. - С. 3113-3124.
  187. Spanos P. D., Muscolino G. Stochastic averaging of Preisach hysteretic systems// J. Engrg. Mech. - 2004. - 130. - С. 1257-1267.
  188. Stoner E. C., Wohlfarth E. P. A mechanism of magnetic hysteresis in heterogeneous alloys// Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. - 1948. - 240. - С. 599-642.
  189. Szabo´ Z., Fu¨zi J. Implementation and identification of Preisach type hysteresis models with Everett function in closed form// J. Magnetism Magnet. Mater. - 2016. - 406. - С. 251-258.
  190. Tabor M. Chaos and integrability in nonlinear dynamics: an introduction. - London: Wiley-Interscience, 1989.
  191. Tak´acs J. The Everett integral and its analytical approximation// В сб.: «Advanced Magnetic Materials». - INTECH, 2012. - С. 203-230.
  192. Tannous C., Gieraltowski J. A Stoner-Wohlfarth model redux: static properties// Phys. B. Cond. Matt. - 2008. - 403. - С. 3563-3570.
  193. Tsabedze T., Zhang J. Design, characterization, modeling, and comparison of helically wrapped supercoiled polymer artificial muscles// Sensors Actuators A. Phys. - 2021. - 331. - С. 113018.
  194. Urbanaviˇciu¯te˙ I., Cornelissen T. D., Meng X., Sijbesma R. P., Kemerink M. Physical reality of the Preisach model for organic ferroelectrics// Nature Commun. - 2018. - 9, № 1. - С. 1-11.
  195. Venegas P., Go´mez D., Arrinda M., Oyarbide M., Macicior H., Bermu´dez A. Kalman filter and classical Preisach hysteresis model applied to the state of charge battery estimation// Comput. Math. Appl. - 2022. - 118. - С. 74-84.
  196. Visintin A. Evolution problems with hysteresis in the source term// SIAM J. Math. Anal. - 1986. - 17.- С. 1113-1138. - doi: 10.1137/0517079.
  197. Visintin A. Differential models of hysteresis. - Springer, 1994.
  198. Visintin A. Ten issues about hysteresis// Acta Appl. Math. - 2014. - 132. - С. 635-647. - doi: 10.1007/s10440-014-9936-6.
  199. Visone C., Serpico C., Mayergoyz I. D., Huang M. W., Adly A. A. Neural-Preisach-type models and their application to the identification of magnetic hysteresis from noisy data// Phys. B. Cond. Matt. - 2000. - 275. - С. 223-227.
  200. Weiss P., de Freudenreich J. E´tude de l’aimantation initiale en fonction de la temp´erature// Arch. Sci. Phys. Natur. - 1916. - 42. - С. 449-470.
  201. Yevstafyeva V. V. Criterion for the existence of two-point oscillatory solution of a perturbed system with a relay// Math. Notes. - 2023. - 114, № 1. - С. 212-222. - doi: 10.1134/S0001434623070222.
  202. Zhang K., Zhao T., Fujiwara H. Training effect of exchange biased iron-oxide/ferromagnet systems// J. Appl. Phys. - 2001. - 89. - С. 6910-6912.

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