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

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      https://www.ias.ac.in/article/fulltext/pram/052/06/0561-0577

    • Keywords

       

      Duffing-van der Pol oscillator; coarse-grained local expansion rates; coarse-grained state variable; weak and strong chaos

    • Abstract

       

      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.

    • Author Affiliations

       

      V Chinnathambi1 S Rajasekar1 2

      1. Department of Physics, AKGS Arts College, Srivaikundam - 628 619, India
      2. Department of Physics, Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli - 627 012, India
    • Dates

       
  • Pramana – Journal of Physics | News

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