Three-Dimensional Space Chaotic Scrolls Generated by Memristive Hopfield Neural Network and Its Application in Robot Path Planning

In this paper, a novel three-dimensional space-scroll chaotic attractor is constructed by introducing piece-wise linear memristors into a three-neurons-based Hopfield neural network to simulate the electromagnetic influence on neural dynamics. The dynamical behaviors of the novel memristive Hopfield neural network are discussed by means of numerical methods including the Lyapunov exponent spectrum, bifurcation diagrams, phase plots and dynamic maps. Furthermore, we also investigated different neurons subject to the memristive electromagnetic influence, where the two-dimensional grid-scroll chaotic attractors can be generated by one neuron subjects to the electromagnetic influence and three-dimensional space-scroll chaotic attractors can be generated by all of the neurons subject to the memristive electromagnetic influence. Moreover, we present a three-dimensional space-scroll scroll attractor-based chaotic mobile robot system. Superiority of the proposed space-scroll-based chaotic mobile robot system compared to existing methods has been demonstrated through numerical simulations.