Vol 32, No 1 (2024)

In 2023, the Department of Dynamic Systems of Saratov State University on the basis of the Saratov branch of the Institute of Radio Engineering and Electronics of the Russian Academy of Sciences turned 25 years old. During this time, the department prepared training courses "Nonlinear oscillations," "Theory of catastrophes," "Dynamic systems and bifurcations," "Dynamic chaos," "Mathematical methods of nonlinear physics" and others. A series of textbooks and taskbooks in the relevant areas has been released.

The purpose of this work is to analyse qualitative features of the information transmission process via several communication schemes based on the synchronization of transmitter and receiver, both being complex signal generators. For this purpose generators of the hyperbolic chaos and generators with the strange nonchaotic attractor are employed. Evaluation of advantages and disadvantages of such schemes is made comparing themselves with each other as well as with schemes based on the nonhyperbolic chaotic generators. Methods. The power spectra and the distributions of the largest finite-time Lyapunov exponent are used to confirm the complexity of the dynamics of the generators in use and to verify the wide-bandness, robustness and stochasticity of their signals. Confidentiality of the informational signal transmission is achieved using its nonlinear mixing to the dynamics of the transmitter. The special phase mixing is used since the model generators employed for the research demonstrate nontrivial dynamics for the angular variable — oscillations phase shift. The digital image is used as an information for transmission. Visual control during the transmission process allows to carry out the qualitative analysis of the success of the signal coding and its detecting by the receiver. Results. Successful transmission and decoding of information for all schemes under investigation are demonstrated for the case of identical transmitter and receiver. Parameter detuning of these generators leads to difficulties in separation of the informational signal from the chaotic/complex carrier due to loss of the full synchronization. For the nonhyperbolic chaos detuning of the parameter responsible for the amplitude of the signal leads to the bad quality of the detection while frequency detuning makes detection absolutely impossible. Schemes with the hyperbolic chaos and strange nonchaotic dynamics appear to demonstrate much better results. The information detection is much better in this case because of the robustness of the generalized synchronization. Conclusion. Robust chaotic and complex nonchaotic generators appear to have significant advantages for communication systems comparing to the chaotic generators of nonhyperbolic type.

Purpose. Investigation of the joint manifestation of the effects of anisotropic signal propagation, coupling, and nonlinear power dependence of the medium parameters in a lattice of laterally and vertically coupled spin-wave (SW) microwaveguides. Consideration of the case of the influence of the rotation of the magnetization angle and the change of the lateral gap between microwaveguides located on the same substrate on the transverse profile of the spin-wave beam and the spatial localization of the SW amplitude. Methods. The method of micromagnetic modeling based on the numerical solution of the Landau–Lifshitz–Hilbert equation shows the possibility of controlling the direction of propagation of SW in an ensemble of laterally and vertically coupled iron yttrium garnet (YIG) microwaveguides by changing the magnetization angle. By the method of numerical integration of the system of coupled discrete nonlinear Schrodinger equations, the possibility of changing the transverse profile of the spin-wave beam by changing the level of the initial signal amplitude is shown. Results. The spatial distributions of the components of the dynamic magnetization of the SW excited in two microwaveguides located on the same substrate obtained in micromagnetic simulations indicate a change in the character of localization of the SW power in the output sections of the microwaveguides. At variation of the lattice magnetization angle, a shift of the threshold power value is observed, at which a characteristic curbing of the transverse width of the spin-wave beam in the nonlinear mode appears. Conclusion. When excitation of surface magnetostatic SW in a lattice of laterally and vertically coupled microwaveguides, a transformation of the transverse profile of the wave is observed at a deviation of the magnetization angle of the structure by 15º , which is manifested in the change of the SW length and its localization in each of the microwaveguides. The combined effects of dipole coupling, gyrotropy, and nonlinearity of the medium make it possible to control the value of the threshold power of the SW, at which the mode of diffractionless propagation of the spin-wave beam is realized in a single layer of the structure.

The aim of the study is to investigate the features of synchronization in ensembles of nonidentical neuron-like FitzHugh–Nagumo oscillators interacting via memristor-based coupling. Methods. The collective dynamics in a ring of FitzHugh–Nagumo oscillators connected via memristive coupling was studied numerically and experimentally. The nonidentity of oscillators was achieved by detuning them by the threshold parameter responsible for the excitation of oscillator, or by detuning them by the parameter characterizing the ratio of time scales, the value of which determines the natural frequency of oscillator. We investigated the synchronization of memristively coupled FitzHugh–Nagumo oscillators as a function of the magnitude of the coupling coefficient, the initial conditions of all variables, and the number of oscillators in the ensemble. As a measure of synchronization, we used a coefficient characterizing the closeness of oscillator trajectories. Results. It is shown that with memristive coupling of FitzHugh–Nagumo oscillators, their synchronization depends not only on the magnitude of the coupling coefficient, but also on the initial states of both the oscillators themselves and the variables responsible for the memristive coupling. We compared the synchronization features of nonidentical FitzHugh–Nagumo oscillators with memristive and diffusive couplings. It is shown that, in contrast to the case of diffusive coupling of oscillators, in the case of meristive coupling, with increasing coupling strength of the oscillators, the destruction of the regime of completely synchronous in-phase oscillations can be observed, instead of which a regime of out-of-phase oscillations appears. Conclusion. The obtained results can be used when solving the problems of synchronization control in ensembles of neuronlike oscillators, in particular, for achieving or destroying the regime of in-phase synchronization of oscillations in an ensemble of coupled oscillators.

The purpose of this work is to study numerically the influence of additive white Gaussian noise on the dynamics of a network of nonlocally coupled neuron models which are represented by FitzHugh–Nagumo oscillators. Depending on coupling parameters between the individual elements this network can demonstrate various spatio-temporal structures, such as chimera states, solitary states and regimes of their coexistence (combined structures). These patterns exhibit different responses against additive noise influences. Methods. The network dynamics is explored by calculating and plotting snapshots (instantaneous spatial distributions of the coordinate values at a fixed time), space-time diagrams, projections of multidimensional attractors, mean phase velocity profiles, and spatial distributions (profiles) of cross-correlation coefficient values. We also evaluate the cross-correlation coefficient averaged over the network, the mean number of solitary nodes and the probability of settling spatio-temporal structures in the neuronal network in the presence of additive noise. Results. It has been shown that additive noise can decrease the probability of settling regimes of solitary states and combined structures, while the probability of observing chimera states arises up to 100%. In the noisy network of FitzHugh–Nagumo oscillators exhibiting the regime of solitary states, increasing the noise intensity leads, in general case, to a decrease of the mean number of solitary nodes and the interval of coupling parameter values within which the solitary states are observed. However, there is a finite region in the coupling parameter plane, inside which the number of solitary nodes can grow in the presence of additive noise. Conclusion. We have studied the impact of additive noise on the probability of observing chimera states, solitary states and combined structures, which coexist in the multistability region, in the network of nonlocally coupled FitzHugh–Nagumo neuron models. It has been established that chimera states represent more stable and dominating structures among the other patterns coexisting in the studied network. At the same time, the probability of settling regimes of solitary states only, the region of their existence in the coupling parameter plane and the number of solitary nodes generally decrease when the noise intensity increases.