Complex Dynamics of 4D Hopfield-Type Neural Network with Two Parameters

Abstract

In this paper, a novel four-dimensional (4D) autonomous continuous time Hopfield-type neural network with two parameters is investigated. Computer simulations show that the 4D Hopfield neural network has rich and funny dynamics, and it can display equilibrium, periodic attractor, chaotic attractor and quasi-periodic attractor for different parameters. Moreover, when the system is chaotic, its positive Lyapunov exponent is much larger than those of the chaotic Hopfield neural networks already reported. The complex dynamical behaviors of the system are further investigated by means of Lyapunov exponents spectrum, bifurcation analysis and phase portraits.