Novel method to detect Hopf bifurcation in a delayed fractional-order network model with bidirectional ring structure  

作　　者：Shuai Li Chengdai Huang Xinyu Song 

机构地区：[1]School of Mathematics and Statistic Xinyang Normal University Xinyang 464000,P.R.China

出　　处：《International Journal of Biomathematics》2023年第6期209-232,共24页生物数学学报（英文版）

基　　金：This work was supported by the National Natural Science Foundation of China(grant numbers 12071407);the Nanhu Scholars Program for Young Scholars of the Xinyang Normal University.

摘　　要：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 nonidentical neurons,we develop a new algebraic technique to deal with the characteristic equation with e-4st(T is the self-feedback delay)term and thus establish the easy-tocheck 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.

关 键 词：Neural networks DELAYS crossing curves fractional order Hopf bifurcation 

分 类 号：O175[理学—数学]