Reducing neuronal networks to discrete dynamics

PHYSICA D-NONLINEAR PHENOMENA

卷:237

Article

Terman, David^1,2  Ahn, Sungwoo¹  Wang, Xueying¹  Just, Winfried³ 

[1] Ohio State Univ, Dept Math, Columbus, OH 43210 USA

[2] Ohio State Univ, Math Biosci Inst, Columbus, OH 43210 USA

[3] Ohio Univ, Dept Math, Athens, OH 45701 USA

关键词: neuronal networks;    discrete dynamics;    singular perturbation;    nonlinear oscillations;   

DOI  :  10.1016/j.physd.2007.09.011

来源: Elsevier

【 摘 要 】

We consider a general class of purely inhibitory and excitatory-inhibitory neuronal networks, with a general class of network architectures, and characterize the complex firing patterns that emerge. Our strategy for studying these networks is to first reduce them to a discrete model. In the discrete model, each neuron is represented as a finite number of states and there are rules for how a neuron transitions from one state to another. In this paper, we rigorously demonstrate that the continuous neuronal model can be reduced to the discrete model if the intrinsic and synaptic properties of the cells are chosen appropriately. In a companion paper [W. Just, S. Ahn, D. Terman. Minimal attractors in digraph system models of neuronal networks (preprint)], we analyse the discrete model. (c) 2007 Elsevier B.V. All rights reserved.

【 授权许可】

Free