Asymptotics of Relaxation Cycles in the Generalized Logistic Delay Equation

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Abstract

Asymptotic methods are used to study solutions of a modified logistic delay equation containing a large parameter. A result on the existence and stability of a relaxation cycle is given.

About the authors

S. A Kashchenko

Regional Scientific and Educational Mathematical Center of the Yaroslavl State University, Yaroslavl, 150003, Russia;

Author for correspondence.
Email: kasch@uniyar.ac.ru

References

  1. Murray J.D. Mathematical Biology II. Spatial Models and Biomedical Applications. Interdisciplinary Applied Mathematics. V. 18. New York, 2003.
  2. Wu J. Theory and Applications of Partial Functional Differential Equations. Applied Mathematical Sciences. V. 119. New York, 1996.
  3. Kuang Y. Delay Differential Equations with Applications in Population Dynamics. Mathematics in Science and Engineering. V. 191. Boston, 1993.
  4. Wright E.M. A non-linear difference-differential equation // J. f"ur die reine und angewandte Mathematik. 1955. Bd. 194. S. 66-87.
  5. Кащенко С.А., Логинов Д.О. Оценка области глобальной устойчивости состояния равновесия логистического уравнения с запаздыванием // Изв. вузов. Математика. 2020. № 9. C. 39-55.
  6. May R.M. Stability and Complexity in Model Ecosystems. Princeton, 1974.
  7. Кащенко С.А. Бифуркации в логистическом уравнении с запаздыванием и малыми возмущениями // Изв. вузов. Математика. 2020. № 10. C. 47-64.
  8. Oster G., Guckenheimer J. Bifurcation phenomena in population models // The Hopf Bifurcation and Its Applications. Appl. Math. Sci. New York, 1976. V. 19. P. 327-353.
  9. Kashchenko S.A. Asymptotics of the solutions of the generalized Hutchinson equation // Automatic Control and Computer Sciences. 2013. V. 47. P. 470-494.
  10. Кащенко С.А. Динамика моделей на основе логистического уравнения с запаздыванием. М., 2020.
  11. Edwards R.E. Functional Analysis. Theory and Applications. New York, 1965.
  12. Кащенко С.А. Периодические решения нелинейных уравнений, обобщающих логистические уравнения с запаздыванием // Мат. заметки. 2017. Т. 102. С. 216-230.

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