23 Gagarin Avenue, Nizhny Novgorod, 603950,Russia
Lobachevsky State University of Nizhni Novgorod
Pankratova E. V., Kalyakulina A. I.
Environmentally Induced Amplitude Death and Firing Provocation in Large-scale Networks of Neuronal Systems
2016, vol. 21, no. 7-8, pp. 840-848
We study the dynamics of multielement neuronal systems taking into account both the direct interaction between the cells via linear coupling and nondiffusive cell-to-cell communication via common environment. For the cells exhibiting individual bursting behavior, we have revealed the dependence of the network activity on its scale. Particularly, we show that small-scale networks demonstrate the inability to maintain complicated oscillations: for a small number of elements in an ensemble, the phenomenon of amplitude death is observed. The existence of threshold network scales and mechanisms causing firing in artificial and real multielement neural networks, as well as their significance for biological applications, are discussed.
Belykh V. N., Pankratova E. V.
Chaotic dynamics of two Van der Pol–Duffing oscillators with Huygens coupling
2010, vol. 15, no. 2-3, pp. 274-284
We consider a system of two coupled Van der Pol-Duffing oscillators with Huygens coupling as an appropriate model of two mechanical oscillators connected to a movable platform via a spring. We examine the complicated dynamics of the system and study its multistable behavior. In particular, we reveal the co-existence of several chaotic regimes and study the structure of the associated riddled basins.