Memristive Multiring Rulkov Neuron Model With Hyperchaotic Firings and Application to Image Cryptosystem

Memristors can be used to simulate the magnetic induction effect of action potentials in biological neurons. The diversity and complexity of firing patterns generated by existing memristive neuron models remain limited, which hinders their ability to fully characterize the rich electrical activities observed in biological nervous systems. To address this issue, this article introduces a novel memristive multiring Rulkov neuron model (MMRNM) by incorporating a universal discrete memristor into the classical Rulkov neuron model, enabling the investigation of more complex neuronal firing patterns and firing multistability. Dynamical analysis indicates that the MMRNM exhibits abundant firing behaviors, such as periodic firing, chaotic firing, hyperchaotic firing, and firing pattern transitions. Meanwhile, the MMRNM can generate multiring firing patterns with an arbitrary number of rings. Through initial offset boosting control, two types of firing multistability, namely homogeneous and heterogeneous firing multistability, are observed. To verify the performance, an STM32-based hardware platform is designed to capture the firing behaviors experimentally. Finally, a novel encryption scheme is designed by leveraging the chaotic and hyperchaotic sequences of the MMRNM, and performance evaluations demonstrate that the scheme possesses robust security.