Sinusoidal Memristive Neuron Model for Hyperchaotic Dynamics: Microcontroller Implementation and Robust Synchronization via Non-Singular Sliding-Mode Control

Abstract

This study explores a discrete memristive neuron model based on sinusoidal transformation (MBST), filling a gap in chaotic neural network research. By coupling a sinusoidal memristor to a discrete neuron model, the system exhibited improved hyperchaotic dynamics, as confirmed by phase portraits, bifurcation diagrams and Lyapunov spectra. The fixed-point method analyzes stability, whereas linear augmentation effectively controls multi-stability by moving the system to a monostable regime. For synchronization, a master-slave architecture with non-singular sliding-mode control outperforms traditional adaptive methods, ensuring robust coordination between neurons. Hardware validation using an ATmega 2560 microcontroller demonstrated real-time feasibility, with results matching those of numerical simulations. A TFT screen (320x480 pixels) was used to visualize the hyperchaotic dynamics, thereby confirming its practical implementation. The complex and controllable behavior of this model offers perspectives for chaos-based encryption, leveraging its unpredictability and synchronization properties.