Chaos in a three dimensional neural network

摘要

An artificial neural network (ANN) consisting of three neurons has been considered. The equations of control are given by three differential equations (DE) with nonlinear, positive and bounded response functions of he neurons. Bifurcation diagram and three dimensional (3-D) phase portraits of the model show rich dynamics. With the change in synaptic weight and decay rate, the system passes from stable to periodic and hen chaotic regimes. Interestingly, the system returns to periodic regime by further changing the synaptic weight. Computer code to calculate the Lyapunov exponent (LE) has been written to confirm chaos.