Quasi-Periodicity Route to Chaos in Neural Networks

Dynamical properties of a network model composed of N continuous elements with randomly chosen asymmetrical couplings and reduced connectivity are studied numerically. Depending on the connectivity and the strength of the nonlinearity we find stable, quasi-periodic and chaotic solutions. The chaotic state exhibits the typical sensitive dependence on the initial conditions. The line of transition from stationary to time-dependent solutions turns out to be almost independent of N in a wide range of network sizes.