Abstract
In this paper, a new four-variable dynamical system is proposed to set chaotic circuit composed of memristor and Josephson junction, and the dependence of chaotic behaviors on nonlinearity is investigated. A magnetic flux-controlled memristor is used to couple with the RCL-shunted junction circuit, and the dynamical behaviors can be modulated by changing the coupling intensity between the memristor and the RCL-shunted junction. Bifurcation diagram and Lyapunov exponent are calculated to confirm the emergence of chaos in the improved dynamical system. The outputs and dynamical behaviors can be controlled by the initial setting and external stimulus as well. As a result, chaos can be suppressed and spiking occurs in the sampled outputs under negative feedback, while applying positive feedback type via memristor can be effective to trigger chaos. Furthermore, it is found that the number of multi-attractors in the Jerk circuit can be modulated when memristor coupling is applied on the circuit. These results indicate that memristor coupling can be effective to control chaotic circuits and it is also useful to reproduce dynamical behaviors for neuronal activities.
Highlights
Chaos emergence can be observed in complex nonlinear systems [1,2,3]
As confirmed in Ref.[82], the Jerk circuit shown in Eq (11) can find chaotic behavior by setting a = 0.3, b = 0.25, and the number of scroll attractors is dependent on the calculating time
Memristor is used to control the chaotic behaviors in a RCL-shunted Junction circuit by imposing induction current generated from memristor
Summary
Chaos emergence can be observed in complex nonlinear systems [1,2,3]. In a practical way, nonlinear circuits [4,5,6,7] can generate chaotic series by setting appropriate parameters carefully, and it is believed that chaotic systems can be used for secure communication and image encryption [8,9,10,11,12].
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