Global bifurcations in a dynamical model of recurrent neural networks
Anita Windisch, Peter Šimon · Applications of Mathematics · 2022
The dynamical behaviour of a continuous time recurrent neural network model with a special weight matrix is studied.The network contains several identical excitatory neurons and a single inhibitory one.This special construction enables us to reduce the dimension of the system and then fully characterize the local and global codimensionone bifurcations.It is shown that besides saddle-node and Andronov-Hopf bifurcations, homoclinic and cycle fold bifurcations may occur.These bifurcation curves divide the plane of weight parameters into nine domains.The phase portraits belonging to these domains are also characterized.