Multiscroll hidden attractor in memristive autapse neuron model and its memristor-based scroll control and application in image encryption

Abstract

In current neurodynamic studies, memristor models using polynomial or multiple nested composite functions are primarily employed to generate multiscroll attractors, but their complex mathematical form restricts both research and application. To address this issue, without relying on polynomial and multiple nested composite functions, this study devises a unique memristor model and a memristive autapse HR (MAHR) neuron model featuring multiscroll hidden attractor. Specially, the quantity of scrolls within the multiscroll hidden attractors is regulated by simulation time. Besides, a simple control factor is incorporated into the memristor to improve the MAHR neuron model. Numerical analysis further finds that the quantity of scrolls within the multiscroll hidden attractor from the improved MAHR neuron model can be conveniently adjusted by only changing a single parameter or initial condition of the memristor. Moreover, a microcontroller-based hardware experiment is conducted to confirm that the improved MAHR neuron model is physically feasible. Finally, an elegant image encryption scheme is proposed to explore the real-world applicability of the improved MAHR neuron model.