Ordered and Chaotic Phenomena in Two Coupled Forced LCR Oscillators Sharing a Common Nonlinearity

Abstract

This paper suggests a simple mechanism of sharing a common nonlinearity among the linear oscillators to exhibit some interesting phenomena. Here, we present fourth-order nonautonomous circuit capable of showing a large variety of dynamical behaviors in three different modes of operation. In particular, a new phenomenon of coexistence of attractors leading to torus behavior when two identical oscillators sharing a common nonlinearity and many spatio-temporal patterns when more oscillators sharing a nonlinearity are presented. The results of numerical simulations, hardware experimental realization and analytical studies are presented.

Chaotic Dynamics and Application of LCR Oscillators Sharing Common Nonlinearity

“…When the dynamic negative loss conductance is very large, the voltages and currents between the capacitor and inductor become exponentially increasing leading to the chaotic behavior of LCR oscillators [Lindberg & Murali, 1998;Murali et al, 1994]. But when single Chua's diode in its original configuration is shared between two coupled LCR oscillators, the oscillators follow quasiperiodic motions as reported by Santhiah et al [2011] and chaos could not be achieved. The parallel combination of two Chua's diodes can be used to circumvent this deadlock and by doing so the output current of the CNE equals the sum of the currents of individual blocks of Chua's diode.…”

“…The nonlinear dissipative circuit comprising two identical, forced LCR oscillators sharing CNE (Fig. 2), is similar to the one used by Santhiah et al [2011] except for the modification in CNE to generate chaos. The nonlinear element considered in the present work is equivalent to that of a parallel combination of two Chua's diodes to introduce a hike in nonlinearity.…”

Matlab Solutions of Chaotic Fractional Order Circuits

“…estimation of the local load state within the individual constituents as response to an overall applied (far field) load. In an effort to better understand dynamical properties of electronic circuits, their stability features and the impact of various parameters, the fractional order approach seems to be very promising (see for example Das, 2008;Dorčák et al, 2007;Petras, 2006;Santhiah et al, 2011;Trzaska, 2008;Marszałek & Trzaska, 2011): many real dynamical circuits are better characterized by using non-integer order models based on fractional order differential or integral calculations. However, the newly produced nano-devices need superior accuracies and possibilities of correlating their hierarchies to models of the fractional order (Baleanu et al, 2010).…”

On nonlinear dynamic of a non-ideal Duffing system with fractional damping

“…Different models for viscoelastic behaviour applying the concept of fractional derivatives were discussed [4]. Fractional calculus have been applied in several fields like as physics, chemistry, finances, and bioengineering [5][6]. In Ref.…”