The influence of heterogeneous interlayer couplings on the dynamics of a two-layer network of FitzHugh—Nagumo neuron rings
Nataliia N. Nikishina 1, Elena V. Rybalova 1, Tatiana E. Vadivasova 1;
1Saratov State University, Saratov, Russia
Abstract
This paper presents the results of a study of the dynamics of a two-layer network consisting of rings of nonlocally coupled FitzHugh—Nagumo oscillators with an heterogeneous interlayer coupling. At the same time, three types of interlayer coupling are considered: 1) constant in time, but random in space; 2) random in time, but constant in space; 3) random in time and space. The values of the control parameters of the rings were chosen in such a way that, in the absence of interlayer coupling, chimera states were established in the first ring, and solitary states in the second. In the course of the study, maps of regimes were constructed on the "probability of establishing a coupling — coupling strength" parameters plane, as well as maps of the distribution of characteristics showing the degree of synchronization of the rings. These studies helped to identify the values of the interlayer coupling parameters corresponding to the synchronization of the rings or the establishment of certain regimes in them. The results of the study showed that with the high probability of establishing a coupling, a complete synchronization regime is mainly observed in both rings. While with low probabilities of interlayer coupling, each ring either tends to maintain its individual dynamics, or synchronization of rings in incoherent regimes is observed.
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Nataliia Nikishina
Saratov State University
Russia
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