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Slow-fast dynamics in a chaotic system with strongly asymmetric memristive element. (English) Zbl 1448.37126

Summary: We investigate the effect of a memristive element on the dynamics of a chaotic system. For this purpose, the chaotic Chua’s oscillator is extended by a memory element in the form of a double-barrier memristive device. The device consists of \(\text{Au/NbO}_{\text{x}} /\text{Al}_2\mathrm{O}_3/\text{Al}/\text{Nb}\) layers and exhibits strong analog-type resistive changes depending on the history of the charge flow. In the obtained system we observe strong changes in the dynamics of chaotic oscillations. The otherwise fluctuating amplitudes of Chua’s system are disrupted by transient silent states. Numerical simulations and analysis of the extended model reveal that the underlying dynamics possesses slow-fast properties due to different timescales between the memory element and the base system. Furthermore, the stabilizing and destabilizing dynamic bifurcations are identified that are traversed by the system during its chaotic behavior.

MSC:

37N35 Dynamical systems in control
94C05 Analytic circuit theory
70K70 Systems with slow and fast motions for nonlinear problems in mechanics
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