Multistable ReLU-Type Memristive Heterogeneous Neuron Model With Multiscroll Firing Dynamics and Application in Image Secure Communication

Memristors possess unique characteristics, including nano-scale dimensions, non-volatility, programmability and synaptic plasticity, enabling them to simulate biological neuronal synapses. Despite existing memristor-synaptic coupled neuron models demonstrating diverse firing patterns under varying initial conditions, the diversity of their multistable firing behaviors remains limited. To address this issue, a new multistable ReLU-type memristor with a piecewise linear function is proposed to couple FitzHugh–Nagumo (FHN) and Hindmarsh–Rose (HR) neurons, establishing a novel multistable ReLU-type memristive heterogeneous neuron model (MRMHNM). Numerical calculations indicate that this MRMHNM displays rich firing dynamics, including periodic spiking firing, chaotic bursting firing, and multi-scroll firing with adjustable scroll numbers. Significantly, it demonstrates distinct firing multistability, encompassing the homogeneous multistability of initial offset-boosted coexisting single-scroll firings, as well as peculiar behaviors in both homogeneous and heterogeneous coexisting scenarios, where the amount of the heterogeneous and homogeneous firings can theoretically increase without bound. In addition, pattern transitions, phase synchronization and geometrically controllable firing behaviors are also comprehensively revealed and investigated. Moreover, a digital hardware platform based on the STM32 microcontroller is employed to implement and verify these intriguing discoveries. Lastly, using the distinctive multistability and multi-scroll firing dynamics of the MRMHNM, a new image secure communication system is built, and experimental results confirm its excellent reliability and security performance.