Articles written in Pramana – Journal of Physics
Volume 39 Issue 5 November 1992 pp 509-520 Research Articles
The influence of time-dependent periodic optical drive in the Fabry-Perot interferometer system has been investigated using a theoretical model equation. A variety of features such as different routes to chaos, multiperiodic oscillations, coexistence of multiple attractors and mode-locking with devil’s staircase are found to occur for a certain range of parametric values.
Volume 41 Issue 4 October 1993 pp 295-309
This paper investigates the possibility of controlling horseshoe and asymptotic chaos in the Duffing-van der Pol oscillator by both periodic parametric perturbation and addition of second periodic force. Using Melnikov method the effect of weak perturbations on horseshoe chaos is studied. Parametric regimes where suppression of horseshoe occurs are predicted. Analytical predictions are demonstrated through direct numerical simulations. Starting from asymptotic chaos we show the recovery of periodic motion for a range of values of amplitude and frequency of the periodic perturbations. Interestingly, suppression of chaos is found in the parametric regimes where the Melnikov function does not change sign.
Volume 44 Issue 2 February 1995 pp 121-131
In this paper we investigate numerically the possibility of conversion of a chaotic attractor into a nonchaotic but strange attractor in both a discrete system (an one dimensional map) and in a continuous dynamical system — Bonhoeffer—van der Pol oscillator. In these systems we show suppression of chaotic property, namely, the sensitive dependence on initial states, by adding appropriate i) chaotic signal and ii) Gaussian white noise. The controlled orbit is found to be strange but nonchaotic with largest Lyapunov exponent negative and noninteger correlation dimension. Return map and power spectrum are also used to characterize the strange nonchaotic attractor.
Volume 45 Issue 4 October 1995 pp 305-309
The Painlevé analysis is applied to the anharmonic oscillator equation$$\ddot x + d\dot x + Ax + Bx^2 + Cx^3 = 0$$. The following three integrable cases are identified: (i)
Volume 47 Issue 3 September 1996 pp 183-198
Integrability and chaotic behaviour in a two-coupled Duffing oscillators are studied. The coupling is nonlinear. Painlevé test is performed to identify integrable cases of damped- and force-free system. Exact analytical solutions are given for the integrable cases. Effect of external periodic forces for (i) single well with infinite height potential, (ii) potential with a hump at the centre and (iii) single well with finite height hump potential are numerically investigated. Occurrence of multiple attractors and period doubling cascades of coexisting attractors is presented.
Volume 48 Issue 1 January 1997 pp 249-258 Spatio-Temporal Chaos, Synchronization And Control
In this paper we consider the Bonhoeffer-van der Pol (BVP) equation which describes propagation of nerve pulses in a neural membrane, and characterize the chaotic attractor at various bifurcations, and the probability distribution associated with weak and strong chaos. We illustrate control of chaos in the BVP equation by the Ott-Grebogi-Yorke method as well as through a periodic instantaneous burst.
Volume 67 Issue 2 August 2006 pp 351-356 Brief Reports
Bifurcations and chaos in the ubiquitous Duffing oscillator equation with different external periodic forces are studied numerically. The external periodic forces considered are sine wave, square wave, rectified since wave, symmetric saw-tooth wave, asymmetric saw-tooth wave, rectangular wave with amplitude-dependent width and modulus of sine wave. Period doubling bifurcations, chaos, intermittency, periodic windows and reverse period doubling bifurcations are found to occur due to the applied forces. A comparative study of the effect of various forces is performed.
Volume 96, 2022
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