A chaotic discrete-time continuous-state Hopfield network with piecewise-affine activation functions

We construct a chaotic discrete-time continuous-state Hopfield networkwith piecewise-affine nonnegative activation functions and weight matrix with small positive entries. More precisely, there exists Cantor set $ C in the state space such that network has sensitive dependence on initial conditions at states orbit of each as its \omega $-limit set. The approach we use is based tools developed employed recently study topological dynamics piecewise-contractions. parameters are explicitly given.