Bogdanov–Takens bifurcation in a Hopfield network model with bidirectional connection and multiple delays
Aws Ben Hamed, Bassem Ben Hamed · IMA Journal of Mathematical Control and Information · 2015
In this paper, a Hopfield network model with three neurons, bidirectional connection and multiple delays is considered. We aim to show that the connection topology is very important. In fact, we consider the connected weights of this system as bifurcation parameters, and the critical values where a Bogdanov–Takens bifurcation occurs are derived. Using the normal form method and the centre manifold theory, we obtain the normal form of our system and study its dynamical behaviours. Finally, a numerical example is given to demonstrate the validity of the results.