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Various attractors, coexisting attractors and antimonotonicity in a simple fourth-order memristive twin-T oscillator. (English) Zbl 1391.34084

Summary: By replacing the resistor in a Twin-T network with a generalized flux-controlled memristor, this paper proposes a simple fourth-order memristive Twin-T oscillator. Rich dynamical behaviors can be observed in the dynamical system. The most striking feature is that this system has various periodic orbits and various chaotic attractors generated by adjusting parameter \(b\). At the same time, coexisting attractors and antimonotonicity are also detected (especially, two full Feigenbaum remerging trees in series are observed in such autonomous chaotic systems). Their dynamical features are analyzed by phase portraits, Lyapunov exponents, bifurcation diagrams and basin of attraction. Moreover, hardware experiments on a breadboard are carried out. Experimental measurements are in accordance with the simulation results. Finally, a multi-channel random bit generator is designed for encryption applications. Numerical results illustrate the usefulness of the random bit generator.

MSC:

34C60 Qualitative investigation and simulation of ordinary differential equation models
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34D45 Attractors of solutions to ordinary differential equations
34C28 Complex behavior and chaotic systems of ordinary differential equations
94C05 Analytic circuit theory
94A60 Cryptography
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