Elegant homogeneous basin of attraction in two-memristor cyclic Hopfield neural network

Abstract

It has been proved that the conventional cyclic Hopfield neural network (CHNN) with three neurons does not exhibit chaotic kinetics. Recently, a memristive CHNN has been developed to generate chaos by replacing two self-connected resistive weights with two memristor adaptive weights. Can two memristor adaptive weights replace the resistive weights of one self-feedback connection and one coupling connection, respectively? In this study, a two-memristor CHNN (TM-CHNN) is presented to generate chaos and planar homogeneous coexisting attractors. TM-CHNN owns a planar equilibrium set, and its stability is periodically distributed over the two memristor’s initial state plane. Using numerical measures, the bifurcation kinetics and typical attractors are revealed, and the planar homogeneous coexisting attractors boosted by memristor’s initial states and kinetic effects caused by non-memristor’s initial states are studied. The numerical results show that TM-CHNN can exhibit chaotic kinetics, especially produce planar homogeneous three-scroll chaotic and multi-periodic attractors, whose elegant homogeneous basins of attraction have exquisite manifold structures and fractal boundaries, and have complex evolution with the change of the memristor’s initial states and non-memristor’s initial states. Additionally, FPGA hardware device is made for implementing TM-CHNN and planar homogeneous coexisting attractors are acquired experimentally to verify the simulated results.