Affiliation:
1. School of Mathematics and Statistic, Xinyang Normal University, Xinyang 464000, P. R. China
Abstract
In this paper, we formulate and study a fractional-order network model with four neurons, bidirectional ring structure and self-delay feedback. For the scenario of non-identical neurons, we develop a new algebraic technique to deal with the characteristic equation with [Formula: see text] ([Formula: see text] is the self-feedback delay) term and thus establish the easy-to-check criteria to determine the Hopf bifurcation point of self-feedback delay by fixing communication delay in its stable interval. For the scenario of identical neurons, we apply the crossing curves method to the fractional functional equations and thus procure the Hopf bifurcation curve. The obtained results accommodate the fact that the model cannot preserve its stability behavior when the self-feedback delay crosses the Hopf bifurcation point in the positive direction. Finally, we deliberate on the correctness of our methodology through two demonstration examples.
Funder
National Natural Science Foundation of China
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Modeling and Simulation
Cited by
9 articles.
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