Strange attractors in chaotic neural networks

This paper aims to prove theoretically that transiently chaotic neural networks (TCNNs) have a strange attractor, which is generated by a bounded fixed point corresponding to a unique repeller in the case that absolute values of the self-feedback connection weights in TCNNs are sufficiently large. We provide sufficient conditions under which the fixed point actually evolves into a strange attractor by a homoclinic bifurcation, which results in complicated chaotic dynamics. The strange attractor of n-dimensional TCNNs is actually the global unstable set of the repeller, which is asymptotically stable, sensitively dependent on initial conditions and topologically transitive. The existence of the strange attractor implies that TCNNs have a globally searching ability for globally optimal solutions of the commonly used objective functions in combinatorial optimization problems when the size of the strange attractor is sufficiently large.