Memristor-coupled cubic hyperchaotic system, feedback synchronization and its application in image encryption

Discrete memristive chaotic systems play a crucial role in information security, and chaotic synchronization form the bedrock of secure and confidential communication. To enhance the chaotic complexity of the Cubic map, we introduce a memristor-coupled Cubic hyperchaotic system by integrating a discrete absolute memristor model with the Cubic map. The dynamics are thoroughly investigated through attractor phase diagrams, bifurcation diagrams, SE complexity analysis, and diagrams illustrating the distribution of dynamic behaviors. Furthermore, we establish methods for chaos control and nonlinear feedback synchronization for the memristive Cubic map. Leveraging this feedback synchronization, we achieve encrypted transmission of digital images. Simulation results validate the feasibility and robust security of the proposed encrypted transmission scheme.