Scroll-growing/controlling chaotic attractors in cyclic Hopfield neural networks via memristive bridging

Abstract

In this paper, a memristor-based neural network is proposed, which is implemented by two tri-neuron resistive-cyclic Hopfield neural networks (RC-HNNs) via memristive bridging. The memristor-bridged network has a line equilibrium set composed of infinitely many index-2 saddle-foci, but it can produce multi-scroll chaotic attractors contrary to Shil’nikov’s criterion. Complex bifurcation behaviors, scroll-growing chaotic attractors over time, and homogeneous coexisting attractors are revealed by numerical methods. Further, a scroll-control scheme is designed and scroll-controlling chaotic attractors are demonstrated numerically. The results show that the memristor-bridged network can not only generate scroll-growing chaotic attractors over time, but also produce scroll-controlling chaotic attractors by limiting the dynamic range of the internal state of the bridging memristor. Finally, an analog electronic circuit is designed for the memristor-bridged network, and PSIM circuit simulations are used to verify the numerical simulations.