Igor Belykh

30 Pryor Street, Atlanta, GA 30303, USA
Department of Mathematics and Statistics, Georgia State University


Barabash N., Belykh I., Kazakov A. O., Malkin M. I., Nekorkin V., Turaev D. V.
In Honor of Sergey Gonchenko and Vladimir Belykh
2024, vol. 29, no. 1, pp.  1-5
This special issue is dedicated to the anniversaries of two famous Russian mathematicians, Sergey V.Gonchenko and Vladimir N.Belykh. Over the years, they have made a lasting impact in the theory of dynamical systems and applications. In this issue we have collected a series of papers by their friends and colleagues devoted to modern aspects and trends of the theory of dynamical chaos.
Citation: Barabash N., Belykh I., Kazakov A. O., Malkin M. I., Nekorkin V., Turaev D. V.,  In Honor of Sergey Gonchenko and Vladimir Belykh, Regular and Chaotic Dynamics, 2024, vol. 29, no. 1, pp. 1-5
Belykh I., Jalil S., Shilnikov A. L.
We study the emergence of in-phase and anti-phase synchronized rhythms in bursting networks of Hodgkin–Huxley–type neurons connected by inhibitory synapses.We show that when the state of the individual neuron composing the network is close to the transition from bursting into tonic spiking, the appearance of the network’s synchronous rhythms becomes sensitive to small changes in parameters and synaptic coupling strengths. This bursting-spiking transition is associated with codimension-one bifurcations of a saddle-node limit cycle with homoclinic orbits, first described and studied by Leonid Pavlovich Shilnikov. By this paper, we pay tribute to his pioneering results and emphasize their importance for understanding the cooperative behavior of bursting neurons. We describe the burst-duration mechanism of inphase synchronized bursting in a network with strong repulsive connections, induced by weak inhibition. Through the stability analysis, we also reveal the dual property of fast reciprocal inhibition to establish in- and anti-phase synchronized bursting.
Keywords: bursting neurons, synchronization, inhibitory networks, burst duration
Citation: Belykh I., Jalil S., Shilnikov A. L.,  Burst-duration mechanism of in-phase bursting in inhibitory networks, Regular and Chaotic Dynamics, 2010, vol. 15, nos. 2-3, pp. 146-158

Back to the list