Global searching ability of chaotic neural networks

Abstract — This paper aims to theoretically prove that both transiently chaotic neural networks (TCNN’s) and discrete-time recurrent neural networks (DRNN’s) have a global attracting set which ensures that the neural networks carry out a global search. A significant property of TCNN’s and DRNN’s is that their attracting sets are generated by a bounded fixed point, which is the unique repeller when absolute values of the self-feedback connection weights in TCNN and the difference time in DRNN are sufficiently large. We provide sufficient conditions under which the neural networks have a trapping region where the global unstable set of the fixed point actually evolves into a global attracting set. We also prove the coexistence of an attracting set and a transversal homoclinic orbit in the same region, which may result in complicated chaotic dynamics. For combinatorial optimization with neural networks, this paper shows that TCNN’