Analyzing stability of equilibrium points in neural networks: a general approach

Authors:
Wilson A. Truccolo;Govindan Rangarajan;Yonghong Chen;Mingzhou Ding
Affiliations:
Department of Neuroscience, Brown University, Providence, RI;Department of Mathematics and Centre for Theoretical Studies, Indian Institute of Science, Bangalore 560 012, India;Xi' an Jiaotong University, Xi' an 710049, China and Center for Complex Systems and Brain Sciences, Florida Atlantic University, Boca Raton, FL;Center for Complex Systems and Brain Sciences, Florida Atlantic University, Boca Raton, FL
Venue:
Neural Networks
Year:
2003

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Abstract

Networks of coupled neural systems represent an important class of models in computational neuroscience. In some applications it is required that equilibrium points in these networks remain stable under parameter variations. Here we present a general methodology to yield explicit constraints on the coupling strengths to ensure the stability of the equilibrium point. Two models of coupled excitatory-inhibitory oscillators are used to illustrate the approach.