Articles written in Pramana – Journal of Physics

    • Bifurcation structure and Lyapunov exponents of a modulated logistic map

      K P Harikrishnan V M Nandakumaran

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      We have studied the bifurcation structure of the logistic map with a time dependant control parameter. By introducing a specific nonlinear variation for the parameter, we show that the bifurcation structure is modified qualitatively as well as quantitatively from the first bifurcation onwards. We have also computed the two Lyapunov exponents of the system and find that the modulated logistic map is less chaotic compared to the logistic map.

    • 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


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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.

    • Complex bifurcation patterns in a discrete predator–prey model with periodic environmental modulation


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      We consider the simplest model in the family of discrete predator–prey system and introduce for the first time an environmental factor in the evolution of the system by periodically modulating the natural death rateof the predator.We show that with the introduction of environmental modulation, the bifurcation structure becomes much more complex with bubble structure and inverse period doubling bifurcation. The model also displays the peculiar phenomenon of coexistence of multiple limit cycles in the domain of attraction for a given parameter value that combine and finally gets transformed into a single strange attractor as the control parameter is increased. To identify the chaotic regime in the parameter plane of the model, we apply the recently proposed scheme based onthe correlation dimension analysis. We show that the environmental modulation is more favourable for the stable coexistence of the predator and the prey as the regions of fixed point and limit cycle in the parameter plane increase at the expense of chaotic domain.

    • Chaos in a cyclic three-species predator–prey system with a partial consumption of superpredator


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      This paper aims at the detailed numerical analysis of a cyclic three species predator–prey model where the prey consumes only a part of the super-predator population. Such a model exists only when the prey acts as an omnivore. Here, we have investigated the dynamical behaviour of the prey, middle predator and super-predator. All the possible equilibrium points of the model are computed and the existence and stability condition of the equilibrium states are determined. The phase portraits are generated for different sets of parameter values. The long term behaviour of the system is investigated by studying the bifurcation structure and nature of the attractors, thereby identifying the domain of chaos, as each of the control parameter is varied independently. Finally, we show that a transition from chaotic domain to escape or vice-versa of the predator in a small region of the parameter plane leads to a fractal structure.

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