Analysis of the complexity and dynamical characteristics of chaotic systems under different memristor models

Abstract Incorporating memristors into nonlinear systems can significantly enhance their dynamical complexity. However, in certain classes of memristor-based nonlinear systems, linear dependencies among variables persist, which substantially diminish their nonlinear characteristics. To overcome this limitation, we propose a novel memristor model and integrate it into two nonlinear systems that originally exhibit linear relationships among variables, effectively increasing system complexity. MATLAB simulations confirm the memristive behavior of the proposed model, while Multisim circuit simulations validate its physical realizability. By replacing the original memristor models in the two systems with the new model, nonlinear analyses of the four resulting systems demonstrate the elimination of the linear dependencies present in the original systems. Bifurcation and Lyapunov exponent analyses reveal that the new memristor systems exhibit chaotic behavior over a broader parameter range with larger Lyapunov exponents. Furthermore, spectral entropy analysis indicates that the new models achieve higher complexity under certain parameters, making them favorable for secure communication applications. Notably, both memristor-based chaotic systems allow single-parameter control of signal amplitude and polarity, which simplifies engineering implementation using only a sliding rheostat and a single-pole double-throw switch. Finally, Multisim simulations and digital signal processor-based hardware experiments confirm the physical feasibility of the proposed memristor chaotic systems.