Bifurcation of a three-unit neural network
The author considers a class of delay differential equations that models a time-delayed connected network of three neurons without self-feedback. The boundary of the stability region is estimated by discussing the change of the number of eigenvalues with zero real part. Then, the author investigates the existence of bifurcation phenomena of codimension one/two of the trivial equilibrium by considering the intersections of some parameter curves, which correspond to a zero root or pure imaginary roots. Some numerical simulations are given to demonstrate the rich dynamical behavior near the equivariant Pitchfork-Hopf bifurcation points, Hopf-Hopf bifurcation points and some higher codimension bifurcation points. The paper is very interesting and the ideas in this paper can be applied to the investigation of large ring networks.
scientific article; zbMATH DE number 5804950