Chaos in neural networks with a nonmonotonic transfer function

Time evolution of diluted neural networks with a nonmonotonic transfer func tion is analytically described by how equations for macroscopic variables. The macroscopic dynamics shows a rich variety of behaviors: fixed-point, pe riodicity, and chaos. We examine in detail the structure of the strange att ractor and in particular we study the main features of the stable and unsta ble manifolds, the hyperbolicity of the attractor, and the existence of hom oclinic intersections. We also discuss the problem of the robustness of the chaos and we prove that in the present model chaotic behavior is fragile ( chaotic regions are densely intercalated with periodicity windows), accordi ng to a recently discussed conjecture. Finally we perform an analysis of th e microscopic behavior and in particular we examine the occurrence of damag e spreading by studying the time evolution of two almost identical initial configurations. We show that for any choice of the parameters the two initi al states remain microscopically distinct. [S1063-651X(99)14608-7].