Hidden dynamics of memristor-coupled neurons with multi-stability and multi-transient hyperchaotic behavior

The coupling of memristors has been extensively studied in continuous neural models. However, little attention has been given to this aspect in discrete neural models. This paper introduces a Discrete Memristor-Coupled Rulkov Neuron (DMCRN) map, utilizing discrete memristors to estimate synaptic functionality. The proposed model is subjected to theoretical analysis, revealing hidden behaviors within the map. Through numerical methods, the rich and complex dynamical behaviors of the DMCRN map are studied, including hyperchaos, hidden attractors, multi-stability and multi-transient, as well as the firing patterns. Additionally, a simple pseudo-random sequence generator (PRNG) is designed based on the generated hyperchaotic sequences, providing a reference for further applications of DMCRN map. In addition, a digital experiment is implemented on a DSP platform, realizing the DMCRN map and obtaining hyperchaos. Both experimental and numerical results demonstrate that the coupling of discrete memristors allows for the estimation of synaptic connections in neurons, resulting in a more complex and interesting discrete neuron model.