• V Chinnathambi

      Articles written in Pramana – Journal of Physics

    • Statistical dynamics at critical bifurcations in Duffing-van der Pol oscillator

      V Chinnathambi S Rajasekar

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      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 Σn(q) of fluctuations of coarse-grained local expansion rates of nearby orbits has a single peak. However, multiple peaks are found just before and just after the critical bifurcations. On the other hand, Σn (q) associated with the coarse-grained state variable is zero far from the bifurcations. The height of the peak of Σn(q) is found to increase as the control parameter approached the bifurcation point. It is maximum at the bifurcation point. Power-law variation of maximal Lyapunov exponent and the mean value of the state variablex is observed near sudden widening and intermittency bifurcations while linear variation is seen near band-merging bifurcation. The standard deviation of local Lyapunov exponent λ(X,L) and the local mean valuex(L) of the coordinatex calculated after everyL time steps are found to approach zero in the limitL → ∞ asL. Β is sensitive to the values of control parameters. Further weak and strong chaos are characterized using the probability distribution of ak-step difference quantity δxk = xi+kxi.

    • 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

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      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.

    • Nonlinear resonance in Duffing oscillator with fixed and integrative time-delayed feedbacks

      V Ravichandran V Chinnathambi S Rajasekar

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      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.

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