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Shilnikov, Andrey

Professor
Office: 810 Petit Science Center
Phone: (404) 413-6423
Email: ashilnikov@gsu.edu

Biographical Information

Ph.D. University Nizhniy Novgorod, Russia, 1990
Postdoctoral Training: Cambridge University, U.K.
Joint Appointment:
Dept. of Mathematics and Statistics
Faculty of the Center for Nonlinear Science at GA Tech

Research Description

Mathematical and computational neuroscience: models of nonlinear oscillatory activity in individual neurons and neural networks.

Dynamics of individual neurons

Most neurons demonstrate oscillations of the membrane potential either endogenously or due to external perturbations. Deterministic description of primary oscillatory activities, such as tonic spiking and bursting, in neuronal models following the Hodgkin-Huxley formalism is based on the theory of dynamical systems and bifurcations. Mathematically, such a conductance based model belongs to a class of dynamical systems with several distinct time scales. The origin of complex behavioral dynamics and preceding bifurcation sequences in neuronal models are in the primary focus of Dr. Shilnikov’s research group. Dr Shilnikov develops the geometric tools of slow-fast systems and the advanced technique of the global bifurcation theory to model and understand in-depth nonlinear dynamics of neurons.

Bursting rhythmogenesis in neural networks

Bursting is a manifestation of the slow-fast dynamics observed in neuroscience including pathological brain states, central pattern generators controlling animal locomotion. The emergence of synchronous rhythms in neural networks is closely related to temporal characteristics of the coupled neurons due to both their intrinsic properties and types of synaptic coupling, inhibitory and excitatory. When cells are nearby the transition edge between bursting and tonic spiking, the dynamics of the network become highly sensitive to small perturbations due to changes in the architecture of the network and of strength of synaptic coupling. Research of Dr. Shilnikov’s group focuses on synergetic mechanisms of dynamical designation of pacemakers on a network endowing it with flexible synchronization properties leading to the multistability of coexistent bursting rhythms.

Grant Support

National Science Foundation