Observation of Chaotic Beats in a Driven Memristive Chua's Circuit

Abstract

In this paper, a time varying resistive circuit realizing the action of an active three segment piecewise linear flux controlled memristor is proposed. Using this as the nonlinearity, a driven Chua's circuit is implemented. The phenomenon of chaotic beats in this circuit is observed for a suitable choice of parameters. The memristor acts as a chaotically time varying resistor (CTVR), switching between a less conductive OFF state and a more conductive ON state. This chaotic switching is governed by the dynamics of the driven Chua's circuit of which the memristor is an integral part. The occurrence of beats is essentially due to the interaction of the memristor aided self-oscillations of the circuit and the external driving sinusoidal forcing. Upon slight tuning/detuning of the frequencies of the memristor switching and that of the external force, constructive and destructive interferences occur leading to revivals and collapses in amplitudes of the circuit variables, which we refer as chaotic beats. Numerical simulations and Multisim modeling as well as statistical analyses have been carried out to observe as well as to understand and verify the mechanism leading to chaotic beats.

Discontinuity Induced Hopf and Neimark–Sacker Bifurcations in a Memristive Murali–Lakshmanan–Chua Circuit

“…A memristive MLC circuit, constructed by replacing the Chua's diode in the classical Murali-Lakshmanan-Chua circuit with an analog model of an active flux controlled memristor, proposed by [Ishaq Ahamed et al, 2011] as its non-linear element was reported earlier in 2013, refer Ishaq & Lakshmanan [2013]. The schematic circuit is shown in Fig.…”

“…For example, memristor based chaotic circuits and their implementations were described in references [Muthuswamy, 2009;Muthuswamy & Kokate, 2009;Muthuswamy, 2010;Muthuswamy & Chua, 2010]. The existence of chaotic beats in a memristive Chua's circuit was reported in Ishaq Ahamed et al [2011] and hyperchoatic beats, hyperchaos and transient hyperchaos in a memristive Murali-Lakshmanan-Chua (MLC) circuit by Ishaq & Lakshmanan [2013]. The coexistence of infinitely many stable periodic orbits and stable equilibrium points has been reported in memristive oscillators by Messias et al [2010].…”

Memristor based-elements for chaotic circuits

“…(1), was recently derived in Fig. 7(b) of [24] by connecting in anti-parallel two basic sub-circuits. According to our findings, those sub-circuits are electronic implementations of the charge-flux characteristics of memristors with opposite polarity.…”

Characteristics for series and parallel circuits of flux-controlled memristors

“…Nowadays the researches of memristor have attracted widely interest of researchers in physics, materials, electronics, informations and other fields because of their potential applications in chaotic secure communication, artificial neural networks, image processing, intelligent computers, the new memories, and electronic measuring systems. And the researchs on the memristor are mainly in several ways, such as the physical mechanics and mathematical models of memristor [4,5,6,7], the manufacturing methods and new manufacturing processes of memristor [2,5,8,9], the characteristic analyses and the kinetic behaviors of memristors [10,11], and so on.…”