Dynamic characteristic of a new fractional-order chaotic system based on the Hopfield Neural Network and its digital circuit implementation

Abstract

In this paper, based on the principle of activation function between the neurons, we designed a Hopfield neural network (HNN) chaotic system. And then we defined a fractional-order HNN chaotic system by Caputo definition. The solution of the fractional-order HNN chaotic system is calculated by Adomain decomposition method (ADM). Then the dynamic performances of the the fractional-order HNN chaotic system are analyzed through attractor phase diagram, bifurcation diagram, Lyapunov exponent spectrum, fractal dimension, chaotic diagram and SE complexity. In addition the system is digital circuit implemented based on DSP platform. The experimental results show that the fractional-order HNN chaotic system not only has rich dynamic behavior, but also has complex nonlinear phenomena such as attractor coexistence which is sensitive to initial value. Therefore, this system has good potential application value, it can be used as multi-source pseudo-random number generator, and the generated pseudo-random sequence can be used in chaotic cryptography and secure communication.