Narrow Results

We present a detailed investigation of the rich variety of bifurcations and chaos associated with a very simple nonlinear parallel nonautonomous LCR circuit with Chua's diode as its only nonlinear element as briefly reported recently [Thamilmaran et al., 2000]. It is proposed as a variant of the simplest nonlinear nonautonomous circuit introduced by Murali, Lakshmanan and Chua (MLC) [Murali et al., 1994]. In our study we have constructed two-parameter phase diagrams in the forcing amplitude-frequency plane, both numerically and experimentally. We point out that under the influence of a periodic excitation a rich variety of bifurcation phenomena, including the familiar period-doubling sequence, intermittent and quasiperiodic routes to chaos as well as period-adding sequences, occur. In addition, we have also observed that the periods of many windows satisfy the familiar Farey sequence. Further, reverse bifurcations, antimonotonicity, remerging chaotic band attractors, and so on, also occur in this system. Numerical simulation results using Poincaré section, Lyapunov exponents, bifurcation diagrams and phase trajectories are found to be in agreement with experimental observations. The chaotic dynamics of this circuit is observed experimentally and confirmed both by numerical and analytical studies as well PSPICE simulation results. The results are also compared with the dynamics of the original MLC circuit with reference to the two-parameter space to show the richness of the present circuit.

We present the results of a very simple nonlinear nonautonomous parallel LCR circuit which exhibits a rich variety of bifurcations and chaos. This simple experimental chaotic oscillator is made up of a few passive components and a uniquely designed nonlinear element comprising of a junction diode and Op-amp based negative conductor. The system exhibits a rich dynamics such as chaos via torus breakdown, period-doubling, period three-doubling, period-adding, Farey sequences, etc., and the results of the investigation are vividly presented along with experimental, numerical and analytical evidences. The laboratory experimental outcomes are in agreement with the numerical and analytical results.

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.

We introduce a simple parametrically driven dissipative second-order chaotic circuit. In this circuit, one of the circuit parameters is varied by an external periodic control signal. Thus by tuning the parameter values of this circuit, classic period-doubling bifurcation route to chaos is found to occur. The experimentally observed phenomena is further validated through corresponding numerical simulation of the circuit equations. The periodic and chaotic dynamics of this model is further characterized by computing Lyapunov exponents.

In this paper, we report the dynamical behaviors of a four-dimensional autonomous system, that is, the modified canonical Chua's circuit. An interesting transition of three-tori–period-3 doubling–chaos is observed when the circuit parameters are varied in the range of our choice. Furthermore, the detailed numerical studies of the system behavior with supporting PSPICE simulations and hardware experiments are also presented here.