Robust chaos in neural networks

We consider the problem of creating a robust chaotic neural network. Robustness means that chaos cannot be destroyed by arbitrary small change of parameters [Phys. Rev. Lett. 80 (1998) 3049]. We present such networks of neurons with the activation function f(x) = \tanh s(x - c)\. We show that in a certain range of s and c the dynamical system x(k+1) = f(x(k)) cannot have stable periodic solutions, which proves the robustness. We also prove that chaos remains robust in a network of weakly connected such neurons. In the end, we discuss ways to enhance the statistical properties of data generated by such a map or network. (C) 2000 Elsevier Science B.V. All rights reserved.