Design and application of spatial multi-structure hidden attractors in memristor-coupled heterogeneous neural networks

Abstract

Biomimetic modeling, through memristors coupling different numbers of heterogeneous neurons, holds extraordinary significance for exploring brain science. To expand the diversity of models related to multi-structure attractors, this paper first proposes a novel multi-segment memristor, and then uses it to couple a 4D Hopfield neural network (HNN) and a 2D Hindmarsh-Rose (HR) neuron. This coupling method simulates the electromagnetic induction effect and mutual-synapses between neurons, thereby constructing a new type of memristor-coupled heterogeneous neural network (MCH-NN) with multi-structure chaotic attractors. This innovative model provides a new perspective for exploring multi-structure behaviors in neural networks. Theoretical research and numerical simulations indicate: (1) In the analysis of the generation mechanism of multi-structure chaotic attractors, its rare hidden characteristics are revealed. (2) This is the first time that arbitrarily controllable quantities of 1D (unidirectional)-, 2D (grid)-, and 3D (spatial)- multi-structure hidden attractors (MSHAs) have been detected in heterogeneous neural networks. Notably, the number of MSHAs is determined by the control parameters of the memristor. (3) The coupling strength significantly affects the dynamic evolution of MCH-NN, and dual-parameter dynamic evolution analysis further confirms this. (4) MCH-NN exhibits rich hidden dynamic characteristics, such as spatial initial offset and spatial amplitude control. Interestingly, mirror-symmetric and mirror-asymmetric MSHAs were also discovered when adjusting the amplitude control parameters. Furthermore, its practical feasibility is validated through analog circuit and digital hardware experiments. Finally, based on MCH-NN, incorporating adaptive filtering denoising technology and spread spectrum communication technology, a novel chaos shift keying (CSK) secure communication scheme is designed, and is intended for binary digital information transmission under low signal-to-noise ratio (SNR) environments. The results demonstrate that this scheme has strong anti-noise performance and excellent communication capabilities.