Discrete bidirectional memristive neural network-based hyperchaotic system and its FPGA implementation.

Abstract

Memristors, owing to their unique non-volatile and nonlinear characteristics, have been widely used to construct biomimetic neural network models. In recent years, discrete-time memristive neural networks (DMNN) have demonstrated significant research value and application potential in the field of chaotic dynamics. However, in existing designs on DMNN-based chaotic systems, there are no relevant reports on the use of novel neural network models with bidirectional feedback structures. In this paper, we propose a hyperchaotic system based on a discrete bidirectional memristive neural network (DBMNN) and implement it on an FPGA platform. A discrete locally active memristor is embedded into the feedback path of a discrete bidirectional neural network (DBNN), forming a six-dimensional DBMNN. The dynamical behavior of DBMNN is theoretically and experimentally studied using various dynamical analysis methods, including equilibrium point analysis, phase diagrams, Lyapunov exponent analysis, bifurcation diagrams, and bi-parameter dynamic maps. The results show that the system exhibits complex chaotic characteristics, including hyperchaos with four positive Lyapunov exponents, heterogeneous coexisting attractors, transient chaos, and chaotic attractor jumping. A large range of amplitude control phenomena is also found. Finally, the circuit design of DBMNN is implemented on a field-programmable gate array (FPGA), and the experimental results are consistent with the numerical simulations, verifying the dynamics of the proposed hyperchaotic system.