Dynamics in Four-Neuron Bidirectional Associative Memory Networks with Inertia and Multiple Delays

Bidirectional associative memory (BAM) networks play an important role in various fields such as optimization, pattern recognition, classification, signal and image processing, parallel computation and associative memory. In this paper, four-neuron BAM networks with inertia and multiple delays are considered. By analyzing the distribution of the eigenvalues of the associated characteristic transcendental equation, local stability criteria are obtained for various system parameters and time delays. By choosing the sum of time delays as a bifurcation parameter, we found that Hopf bifurcation occurs when the sum of time delays passes through a sequence of critical values. Some explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions are obtained by using the normal form theory and center manifold theory. Some numerical simulations are carried out to support theoretical predictions. Our results are new and supplement some previously known studies.