Bifurcation analysis in a recurrent neural network model with delays
The aim of this paper is to investigate the dynamical behavior of a three-node recurrent network model with four discrete time delays. After the introduction, the stability of the trivial equilibrium and the existence of several types of bifurcation are analyzed in Section 2. Using the method of multiple time scales (MTS), the authors derive in Section 3 the normal form of a nonlinear differential equation system associated with the Hopf-zero bifurcation, while Section 4 obtains the normal forms for non-resonant Hopf bifurcations. Section 5 studies the Hopf-zero bifurcation and double Hopf bifurcation, providing the corresponding critical points. Numerical simulations are presented for the verification of the analytical approach. In particular, for the resonant double Hopf bifurcation, numerical expressions for certain parameter values are found, although a closed-form solution of the non-trivial steady-state solutions is difficult to be obtained. The observed concordance between the analytical predictions and numerical simulations for the solutions of amplitude and frequency shows that the proposed method provides an efficient tool for the study of real problems.
scientific article; zbMATH DE number 6117612