Hopf-Pitchfork Bifurcation Analysis of a Coupled Neural Oscillator System with Excitatory-to-Inhibitory Connection and Time Delay
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Springer International Publishing AG, part of Springer Nature 2018. In this paper, a coupled neural oscillator system with excitatory-to-inhibitory connection and time delay is considered. First, the existence of pitchfork bifurcation and the equilibrium patterns are investigated. It is found that the system has one, three and five equilibria with self-connection weight increasing. Then, by choosing the self-connection weight and communication delay as the two bifurcation parameters, the conditions where Hopf-pitchfork bifurcation occurs are obtained. Analyzing the bifurcation diagram, we find that the system exhibits many complex phenomena such as co-existence of two synchronous equilibria or two anti-synchronous equilibria, two stable periodic solutions, and two quasi-periodic attractors, which are validated by numerical simulations.
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
author list (cited authors)
Yang, L., Dong, T., & Huang, T.