Physics Letters A 277 (2000) 310–322 www.elsevier.nl/locate/pla 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 / D j tanh s.x c/j. We show that in a certain range of s and c the dynamical system xkC1 D f.xk/ 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