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. 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. 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. Moreover, the period-doubling route to chaos and crisis phenomena are observed too. Furthermore, the hysteresis phenomenon, as well as the existence of coexisting attractors in regards to the initial conditions and the parameters of the system, are investigated. More specifically, the entrance to chaotic behavior through the antimonotonicity phenomenon is observed. Interesting phenomena related to chaos theory are observed. In order to examine the circuit’s dynamical behavior, a host of nonlinear simulation tools, such as phase portraits, bifurcation and continuation diagrams, as well as a maximal Lyapunov exponent diagram, are used. Consequently, for the first time, the KNOWM memristor is used as a static nonlinear resistor in the well-known chaotic Shinriki oscillator. ![]() Furthermore, this memristor has been shown to act like a static nonlinear resistor under certain situations. ![]() ![]() The KNOWM’s memristor’s intrinsic feature encourages its use as a nonlinear resistor in chaotic circuits. A novel approach to the physical memristor’s behavior of the KNOWM is presented in this work.
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