Lyapunov exponents and mutual information of chaotic neural networks

Lyapunov exponents and mutual information are calculated for a simple chaotic neuron map and 1D nearest neighbour coupling networks. To understand the associative dynamics created by coupled neurons is important. To measure these dynamics, we employ the largest Lyapunov exponent and spatial and temporal mutual information. We find that the largest Lyapunov exponent can increase as the weight of coupling increases, even if network dynamics includes spatial coupling. Because of this fact, the largest Lyapunov exponent of a network may exceed the Lyapunov exponent of a neuron. We also find that the largest Lyapunov exponent of networks may decrease as the Lyapunov exponent of single neurons increases. This result conflicts with the result of intensive studies of the coupled logistic map. Spatial and temporal informations decay exponentially with spatial distance and time-step, respectively. The rate of exponential decay decreases as the largest Lyapunov exponent decreases. These properties match the results of the coupled logistic map