Natalia Shchegoleva
Publications:
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Stankevich N. V., Bobrovsky A. A., Shchegoleva N. A.
Chaos and Hyperchaos in Two Coupled Identical Hindmarsh – Rose Systems
2024, vol. 29, no. 1, pp. 120-133
Abstract
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.
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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
Abstract
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.
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