Synchronization control of memristive chaotic maps based on Rulkov neuron models and their application in traffic image protection

Abstract

This paper proposes a memristive Rulkov map (MRM) by designing a memristor controlled by a single function to achieve odd–even expansions of chaotic attractors, forming one-dimensional (1D-MRM) and two-dimensional (2D-MRM) models. The 1D-MRM demonstrates flexible amplitude control, pseudo-symmetry in parameter complexity, and extreme multistability, while the 2D-MRM realizes attractor replication and exhibits synchronization among subsystems. Based on this, an adaptive projection synchronization control method for heterogeneous systems is developed. Furthermore, a thumbnail-based image encryption algorithm is designed using this synchronization scheme, which employs a JK-like flip-flop diffusion rule and a 3D cubic matrix for cross-channel scrambling and diffusion. Experimental results confirm the algorithm's high performance and robustness in traffic image protection.