Exploring the dynamics of a multistable general model of discrete memristor-based map featuring an exponentially varying memristance.

Chua's groundbreaking discovery in 1971 introduced the memristor as the fourth essential electrical component, joining resistance, capacitance, and inductance. Over the past few years, numerous discrete memristor models have been developed following its formal proposal, expanding our understanding of this subject. However, there is limited discussion about multistable discrete memristor models. This research combines a comprehensive methodology for generating memristive maps using the modulo function and an exponential memristance, resulting in the development of a multistable discrete memristor model. Nonlinear techniques, such as bifurcation diagrams, Lyapunov spectrum diagrams, and phase portraits were utilized to analyze the dynamic characteristics of the system. The findings uncovered a range of captivating phenomena associated with chaos theory, including regular orbits, chaotic orbits, the mechanism of period doubling leading to chaos, crisis phenomena, and the presence of multistability. • Diagrams resembling bifurcation plots with two parameters were used to illustrate the dynamic behavior of the system. • Variations in initial conditions brought to light the presence of coexisting attractors. • Modified general discrete memristor model presented multistability under different initial conditions. • The behavior of the memristor as an active element becomes apparent when its internal state assumes smaller values. [ABSTRACT FROM AUTHOR]