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Journal of Vibration Testing and System Dynamics 9(3) (2025) 221--231 | DOI:10.5890/JVTSD.2025.09.002

Laskaridis Lazaros$^{1}$, Christos Volos$^{1}$, Hector Nistazakis$^{2}$, Ioannis Stouboulos$^{1}$

$^{1}$ Laboratory of Nonlinear Systems - Circuits & Complexity, Physics Department, Aristotle University of Thessaloniki, Thessaloniki, Thessaloniki, 54124, Greece

$^{2}$ Section of Electronic Physics and Systems, Department of Physics, National and Kapodistrian University of Athens, Athens 15784, Greece

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Abstract

In 1971, Chua discovered the memristor, which is considered the fourth fundamental electrical component alongside resistance, capacitance, and inductance. In recent years, numerous models of discrete memristors have been constructed since the formal proposal of the subject. However, there is rare discussion about the active discrete memristor models. This study combines a general map for constructing memristive maps with the modulo function and an exponential memristance, which produces a locally active discrete memristor model. Nonlinear tools, including bifurcation and continuation diagrams, Lyapunov spectrum diagrams, and phase portraits, were employed to investigate the system's dynamical behavior. The results revealed various intriguing phenomena related to chaos theory, including periodic or chaotic orbits, the mechanism of period doubling route to chaos, crisis phenomena, as well as coexisting attractors.

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