Natalia Shchegoleva

Astrahanskaya 83, Saratov, 410012, Russia
Saratov State University


Stankevich N. V., Bobrovsky A. A., Shchegoleva N. A.
The dynamics of two coupled neuron models, the Hindmarsh – Rose systems, are studied. Their interaction is simulated via a chemical coupling that is implemented with a sigmoid function. It is shown that the model may exhibit complex behavior: quasiperiodic, chaotic and hyperchaotic oscillations. A phenomenological scenario for the formation of hyperchaos associated with the appearance of a discrete Shilnikov attractor is described. It is shown that the formation of these attractors leads to the appearance of in-phase bursting oscillations.
Keywords: neuron model, Hindmarsh – Rose system, chaos, hyperchaos, in-phase bursting
Citation: Stankevich N. V., Bobrovsky A. A., Shchegoleva N. A.,  Chaos and Hyperchaos in Two Coupled Identical Hindmarsh – Rose Systems, Regular and Chaotic Dynamics, 2024, vol. 29, no. 1, pp. 120-133
Kuznetsov A. P., Shchegoleva N. A., Sataev I. R., Sedova Y. V., Turukina L. V.
From Chaos to Quasi-Periodicity
2015, vol. 20, no. 2, pp.  189-204
Ensembles of several Rössler chaotic oscillators are considered. It is shown that a typical phenomenon for such systems is the emergence of different and sufficiently high dimensional invariant tori. The possibility of a quasi-periodic Hopf bifurcation and a cascade of such bifurcations based on tori of increasing dimension is demonstrated. The domains of resonance tori are revealed. Boundaries of these domains correspond to the saddle-node bifurcations. Inside the domains of resonance modes, torus-doubling bifurcations and destruction of tori are observed.
Keywords: chaos, quasi-periodic oscillation, invariant torus, Lyapunov exponent, bifurcation
Citation: Kuznetsov A. P., Shchegoleva N. A., Sataev I. R., Sedova Y. V., Turukina L. V.,  From Chaos to Quasi-Periodicity, Regular and Chaotic Dynamics, 2015, vol. 20, no. 2, pp. 189-204

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