Discrete Memristive Conservative Chaotic Map: Dynamics, Hardware Implementation, and Application in Secure Communication

The randomness of chaotic systems are crucial for their application in secure communication. Conservative systems exhibit enhanced ergodicity and randomness in comparison to dissipative chaotic systems. However, the memristor-based conservative chaotic maps remain unreported. This article presents a study of volume-preserving chaotic maps based on discrete memristor (DM). We propose and analyze a generic conservative map that incorporates DM. The conservative characteristics of the proposed iterative map are confirmed through the determinant of its Jacobian matrix. Furthermore, four distinct DM models are introduced and their memristive characteristics are verified through numerical simulations of hysteresis loops. To investigate the dynamical properties of the discrete memristive conservative map (DMCM), we incorporate the proposed DM models into the generic conservative map model using numerical methods, including phase portraits, Lyapunov exponents, and bifurcation diagrams. Additionally, the hardware implementation of the DMCM on an FPGA platform demonstrates the reliability of the model. Finally, secure communication experiments based on the DMCM show that it outperforms some classical dissipative chaotic maps in terms of bit error rate performance.