Modeling and Analysis of a Three-Terminal-Memristor-Based Conservative Chaotic System

A Robust Memristor-Enhanced Polynomial Hyper-Chaotic Map and Its Multi-Channel Image Encryption Application

Nowadays, the utilization of memristors to enhance the dynamical properties of chaotic systems has become a popular research topic. In this paper, we present the design of a novel 2D memristor-enhanced polynomial hyper-chaotic map (2D-MPHM) by utilizing the cross-coupling of two TiO2 memristors. The dynamical properties of the 2D-MPHM were investigated using Lyapunov exponents, bifurcation diagrams, and trajectory diagrams. Additionally, Kolmogorov entropy and sample entropy were also employed to evaluate the complexity of the 2D-MPHM. Numerical analysis has demonstrated the superiority of the 2D-MPHM. Subsequently, the proposed 2D-MPHM was applied to a multi-channel image encryption algorithm (MIEA-MPHM) whose excellent security was demonstrated by key space, key sensitivity, plaintext sensitivity, information entropy, pixel distribution, correlation analysis, and robustness analysis. Finally, the encryption efficiency of the MIEA-MPHM was evaluated via numerous encryption efficiency tests. These tests demonstrate that the MIEA-MPHM not only possesses excellent security but also offers significant efficiency advantages, boasting an average encryption rate of up to 87.2798 Mbps.

A memcapacitor-based hyperchaotic conservative system

To explore the applications of the memcapacitor in the conservative circuits, the nonlinear dynamics of a memcapacitor-based hyperchaotic conservative circuit are studied in detail. Specifically, the conservative condition of the system is obtained by combining divergence and Hamiltonian energy, and the perpetual points and equilibrium points of the memcapacitor-based system are also analyzed in detail. Subsequently, the influences of system parameters and initial conditions on the dynamics of the memcapacitor-based hyperchaotic conservative system are discussed through the dynamic map and the basin of attraction, where three dynamics phenomena can be observed, such as interior crisis, largest Lyapunov exponent jump, and coexisting conservative flows. Finally, the theoretical results are verified by the circuit experiment simulation through MULTISIM and digital signal processing; a pseudorandom number generator based on the hyperchaotic conservative system is also designed and compared with another system through an NIST test.