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Analysis of a Three-Dimensional Non-autonomous Chaotic Circuit with a Thermistor as a Physical Memristor

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Complex Systems and Their Applications

Abstract

In 1976, Prof. Leon Chua proposed that a physical thermistor can be modeled as a memristive device, which can be used as a nonlinear element in chaotic circuits. In this direction, an autonomous circuit with two passive elements (inductor and capacitor), a nonlinear resistor, and a thermistor, which plays the role of a nonlinear locally active memristor, has been proposed by Ginoux et al. This work presents the study of a non-autonomous circuit, which is based on the aforementioned autonomous circuit, by adding an external voltage AC source. Moreover, the effect of the capacitor’s and inductor’s value and the effect of the initial conditions in system’s dynamical behavior have been studied. To investigate further system’s dynamical behavior, various tools from nonlinear theory have been used, such as bifurcation and maximal Lyapunov exponent diagrams, Poincaré maps, and Kaplan–Yorke dimension. Interesting phenomena related to chaos have been investigated. In more detail, chaotic and regular orbits, such as periodic or semi-periodic, have been observed. Furthermore, the route to chaos through the mechanism of period doubling, coexisting attractors, and crisis phenomena have been observed.

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Correspondence to Laskaridis Lazaros .

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Lazaros, L., Christos, V., Ioannis, S. (2022). Analysis of a Three-Dimensional Non-autonomous Chaotic Circuit with a Thermistor as a Physical Memristor. In: Huerta Cuéllar, G., Campos Cantón, E., Tlelo-Cuautle, E. (eds) Complex Systems and Their Applications. Springer, Cham. https://doi.org/10.1007/978-3-031-02472-6_11

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