Bogdanov-Takens bifurcation in a neutral BAM neural networks model with delays.

Abstract

In this study, the authors first discuss the existence of Bogdanov-Takens and triple zero singularity of a five neurons neutral bidirectional associative memory neural networks model with two delays. Then, by utilising the centre manifold reduction and choosing suitable bifurcation parameters, the second-order and the third-order normal forms of the Bogdanov-Takens bifurcation for the system are obtained. Finally, the obtained normal form and numerical simulations show some interesting phenomena such as the existence of a stable fixed point, a pair of stable non-trivial equilibria, a stable limit cycles, heteroclinic orbits, homoclinic orbits, coexistence of two stable non-trivial equilibria and a stable limit cycles in the neighbourhood of the Bogdanov-Takens bifurcation critical point.