Chaos and hyperchaos in a Hopfield neural network

In this paper we investigate numerically the parameter-space of an autonomous system of four nonlinear first-order ordinary differential equations, which represents a Hopfield neural network with four neurons. The study considers three independent two-dimensional cross-sections of the three-dimensional parameter-space generated by this mathematical model, every constructed considering Lyapunov exponent values. We show that is possible to completely characterize the dynamics of the system based in these three plots, which are representative of the three-dimensional parameter-space as a whole.