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

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.Inspec keywords: neurophysiology, neural nets, bifurcation, delays, critical pointsOther keywords: Bogdanov‐Takens bifurcation critical point, neutral BAM neural networks, bidirectional associative memory, delays, triple zero singularity, neurons, centre manifold reduction, bifurcation parameters, second‐order normal forms, third‐order normal forms, numerical simulations, stable fixed point, stable nontrivial equilibria, stable limit cycles, heteroclinic orbits, homoclinic orbits