S Rajasekar
Articles written in Pramana – Journal of Physics
Volume 52 Issue 6 June 1999 pp 561-577 Research Articles
Statistical dynamics at critical bifurcations in Duffing-van der Pol oscillator
We study the characteristic features of certain statistical quantities near critical bifurcations such as onset of chaos, sudden widening and band-merging of chaotic attractor and intermittency in a periodically driven Duffing-van der Pol oscillator. At the onset of chaos the variance of local expansion rate is found to exhibit a self-similar pattern. For all chaotic attractors the variance Σ_{n}(
Volume 62 Issue 1 January 2004 pp 1-12
Painlevé analysis and integrability of two-coupled non-linear oscillators
Integrability of a linearly damped two-coupled non-linear oscillators equation$$\begin{gathered} \mathop x\limits^{..} = - d\mathop {\mathop x\limits^. - \alpha x - \delta _1 (x^2 + y^2 ) - 2\delta _2 xy}\limits^. \hfill \\ \mathop y\limits^{..} = d\mathop y\limits^. - \beta y - \delta _2 (x^2 + y^2 ) - 2\delta _1 xy \hfill \\ \end{gathered} $$ is investigated by employing the Painlevé analysis. The following two integrable cases are identified: (i)
Volume 72 Issue 6 June 2009 pp 927-937 Research Articles
Role of asymmetries in the chaotic dynamics of the double-well Duffing oscillator
V Ravichandran S Jeyakumari V Chinnathambi S Rajasekar M A F Sanjuán
Duffing oscillator driven by a periodic force with three different forms of asymmetrical double-well potentials is considered. Three forms of asymmetry are introduced by varying the depth of the left-well alone, location of the minimum of the left-well alone and above both the potentials. Applying the Melnikov method, the threshold condition for the occurrence of horseshoe chaos is obtained. The parameter space has regions where transverse intersections of stable and unstable parts of left-well homoclinic orbits alone and right-well orbits alone occur which are not found in the symmetrical system. The analytical predictions are verified by numerical simulation. For a certain range of values of the control parameters there is no attractor in the left-well or in the right-well.
Volume 76 Issue 3 March 2011 pp 373-383
Oscillatory variation of anomalous diffusion in pendulum systems
Numerical studies of anomalous diffusion in undamped but periodically-driven and parametrically-driven pendulum systems are presented. When the frequency of the periodic driving force is varied, the exponent 𝜇, which is the rate of divergence of the mean square displacement with time, is found to vary in an oscillatory manner. We show the presence of such a variation in other statistical measures such as variance of position, kurtosis, and exponents in the power-exponential law of probability distribution of position.
Volume 78 Issue 3 March 2012 pp 347-360 Research Articles
Nonlinear resonance in Dufﬁng oscillator with ﬁxed and integrative time-delayed feedbacks
V Ravichandran V Chinnathambi S Rajasekar
We study the nonlinear resonance, one of the fundamental phenomena in nonlinear oscillators, in a damped and periodically-driven Dufﬁng oscillator with two types of time-delayed feedbacks, namely, ﬁxed and integrative. Particularly, we analyse the effect of the time-delay parameter 𝛼 and the strength 𝛾 of the time-delayed feedback. Applying the perturbation theory we obtain a nonlinear equation for the amplitude of the periodic response of the system. For a range of values of 𝛾 and 𝛼, the response amplitude is found to be higher than that of the system in the absence of delayed feedback. The response amplitude is periodic on the parameter 𝛼 with period $2\pi /\omega$ where 𝜔 is the angular frequency of the external periodic force. We show the occurrence of multiple branches of the response amplitude curve with and without hysteresis.
Volume 81 Issue 1 July 2013 pp 127-141 Research Articles
Vibrational resonance in the Morse oscillator
K Abirami S Rajasekar M A F Sanjuan
The occurrence of vibrational resonance is investigated in both classical and quantum mechanical Morse oscillators driven by a biharmonic force. The biharmonic force consists of two forces of widely different frequencies $\omega$ and $\Omega$ with $\Omega \gg \omega$. In the damped and biharmonically driven classical Morse oscillator, by applying a theoretical approach, an analytical expression is obtained for the response amplitude at the low-frequency $\omega$. Conditions are identified on the parameters for the occurrence of resonance. The system shows only one resonance and moreover at resonance the response amplitude is $1/d\omega$ where $d$ is the coefficient of linear damping. When the amplitude of the high-frequency force is varied after resonance the response amplitude does not decay to zero but approaches a nonzero limiting value. It is observed that vibrational resonance occurs when the sinusoidal force is replaced by a square-wave force. The occurrence of resonance and antiresonance of transition probability of quantum mechanical Morse oscillator is also reported in the presence of the biharmonic external field.
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