Nataliya Stankevich

Nizhny Novgorod, Bolshaya Pecherskaya str. 25/12
HSE 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
Stankevich N. V., Dvorak A., Astakhov V. V., Jaros P., Kapitaniak M., Perlikowski P., Kapitaniak T.
The dynamics of two coupled antiphase driven Toda oscillators is studied. We demonstrate three different routes of transition to chaotic dynamics associated with different bifurcations of periodic and quasi-periodic regimes. As a result of these, two types of chaotic dynamics with one and two positive Lyapunov exponents are observed. We argue that the results obtained are robust as they can exist in a wide range of the system parameters.
Keywords: chaos, hyperchaos, Toda oscillator
Citation: Stankevich N. V., Dvorak A., Astakhov V. V., Jaros P., Kapitaniak M., Perlikowski P., Kapitaniak T.,  Chaos and Hyperchaos in Coupled Antiphase Driven Toda Oscillators, Regular and Chaotic Dynamics, 2018, vol. 23, no. 1, pp. 120-126
Kuptsov P. V., Kuznetsov S. P., Stankevich N. V.
A generalized model with bifurcations associated with blue sky catastrophes is introduced. Depending on an integer index $m$, different kinds of attractors arise, including those associated with quasi-periodic oscillations and with hyperbolic chaos. Verification of the hyperbolicity is provided based on statistical analysis of intersection angles of stable and unstable manifolds.
Keywords: dynamical system, blue sky catastrophe, quasi-periodic oscillations, hyperbolic chaos, Smale–Williams solenoid
Citation: Kuptsov P. V., Kuznetsov S. P., Stankevich N. V.,  A Family of Models with Blue Sky Catastrophes of Different Classes, Regular and Chaotic Dynamics, 2017, vol. 22, no. 5, pp. 551-565

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