• G Ambika

      Articles written in Pramana – Journal of Physics

    • Perturbative evaluation of universal constants for a quartic map

      G Ambika K Babu Joseph

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      We discuss a perturbative scheme for the determination of the bifurcation rate δ for a specific map, by extending Virendra Singh’s method of evaluating the scaling factor α. The method is applied to a quartic map and the values obtained, α = 1.690781026 and δ = 7.23682924 are in good agreement with the numerically computed values reported in the literature. The perturbative approach is found to be more efficient than other existing methods.

    • Use of Padé approximants in the evaluation of α and δ for one-dimensional maps

      G Ambika K M Valsamma

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      Recently an analytic algorithm for evaluating the Feigenbaum indices of one-dimensional maps was developed using a perturbative expansion. We find that the use of Padé approximants in the resulting asymptotic series, significantly improves the technique.

    • Transition to chaos in a driven pendulum with nonlinear dissipation

      G Ambika K Babu Joseph

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      The Melnikov-Holmes method is used to study the onset of chaos in a driven pendulum with nonlinear dissipation. Detailed numerical studies reveal many interesting features like a chaotic attractor at low frequencies, band formation near escape from the potential well and a sequence of subharmonic bifurcations inside the band that accumulates at the homoclinic bifurcation point.

    • Deterministic chaos in one-dimensional maps—the period doubling and intermittency routes

      G Ambika K Babu Joseph

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      This paper is a review of the present status of studies relating to occurrence of deterministic chaos and its characterization in one-dimensional maps. As our primary aim is to introduce the nonspecialists into this fascinating world of chaos we start from very elementary concepts and give sufficient arguments for clarity of ideas. The two main scenarios during onset of chaos viz. the period doubling and intermittency are dealt with in detail. Although the logistic map is often discussed by way of illustration, a few more interesting maps are mentioned towards the end.

    • f-α Spectrum of circle map

      K M Valsamma K Babu Joseph G Ambika

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      We present an analytic perturbative method for calculatingf(α) and the generalized dimensionDq of the critical invariant circle of the polynomial circle map. The scaling behaviour is found to depend onz, the exponent defining the map. The asymptotic bounds of the scaling constantsα(z) andδ(z) are verified analytically.

    • Scaling relations in the lyapunov exponents of one dimensional maps

      P R Krishnan Nair V M Nandakumaran G Ambika

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      We establish numerically the validity of Huberman-Rudnick scaling relation for Lyapunov exponents during the period doubling route to chaos in one dimensional maps. We extend our studies to the context of a combination map, where the scaling index is found to be different.

    • Dynamics of the logistic map under discrete parametric perturbation

      P P Saratchandran V M Nandakumaran G Ambika

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      By introducing a periodic perturbation in the control parameter of the logistic map we have investigated the period locking properties of the map. The map then gets locked onto the periodicity of the perturbation for a wide range of values of the parameter and hence can lead to a control of the chaotic regime. This parametrically perturbed map exhibits many other interesting features like the presence of bubble structures, repeated reappearance of periodic cycles beyond the chaotic regime, dependence of the escape parameter on the seed value and also on the initial phase of the perturbation etc.

    • Chaos in Josephson junctions

      G Ambika

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      A detailed analysis of the control space characterization of phase locked states and chaotic attractors in Josephson junctions is presented, based on a model that includes both quadratic damping and cosine interference terms. In addition, some novel features of the nonlinear characteristics of the junction like evolution of basin boundaries, bifurcation structure analysis and scaling behaviour of Lyapunov exponent are discussed.

    • Bubbling and bistability in two parameter discrete systems

      G Ambika N V Sujatha

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      We present a graphical analysis of the mechanisms underlying the occurrences of bubbling sequences and bistability regions in the bifurcation scenario of a special class of one dimensional two parameter maps. The main result of the analysis is that whether it is bubbling or bistability is decided by the sign of the third derivative at the inflection point of the map function.

    • Critical exponents in the transition to chaos in one-dimensional discrete systems

      G Ambika N V Sujatha

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      We report the numerically evaluated critical exponents associated with the scaling of generalized fractal dimensions during the transition from order to chaos. The analysis is carried out in detail in the context of unimodal and bimodal maps representing typical one-dimensional discrete dynamical systems. The behavior of Lyapunov exponents (LE) in the cross over region is also studied for a complete characterization.

    • Occurrence of stable periodic modes in a pendulum with cubic damping

      K I Thomas G Ambika

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      Dynamical systems with nonlinear damping show interesting behavior in the periodic and chaotic phases. The Froude pendulum with cubical and linear damping is a paradigm for such a system. In this work the driven Froude pendulum is studied by the harmonic balancing method; the resulting nonlinear response curves are studied further for resonance and stability of symmetric oscillations with relatively low damping. The stability analysis is carried out by transforming the system of equations to the linear Mathieu equation.

    • Stochastic resonance and chaotic resonance in bimodal maps: A case study

      G Ambika N V Sujatha K P Harikrishnan

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      We present the results of an extensive numerical study on the phenomenon of stochastic resonance in a bimodal cubic map. Both Gaussian random noise as well as deterministic chaos are used as input to drive the system between the basins. Our main result is that when two identical systems capable of stochastic resonance are coupled, the SNR of either system is enhanced at an optimum coupling strength. Our results may be relevant for the study of stochastic resonance in biological systems.

    • Cross over of recurrence networks to random graphs and random geometric graphs

      RINKU JACOB K P HARIKRISHNAN R MISRA G AMBIKA

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      Recurrence networks are complex networks constructed from the time series of chaotic dynamical systems where the connection between two nodes is limited by the recurrence threshold. This condition makes the topology of every recurrence network unique with the degree distribution determined by the probability densityvariations of the representative attractor from which it is constructed. Here we numerically investigate the properties of recurrence networks from standard low-dimensional chaotic attractors using some basic network measuresand show how the recurrence networks are different from random and scale-free networks. In particular, we show that all recurrence networks can cross over to random geometric graphs by adding sufficient amount of noise tothe time series and into the classical random graphs by increasing the range of interaction to the system size. We also highlight the effectiveness of a combined plot of characteristic path length and clustering coefficient in capturing the small changes in the network characteristics.

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