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By
Krishnan Nair, P R; Nandakumaran, V M; Ambika, G
5 Citations
We establish numerically the validity of HubermanRudnick 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.
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By
Singh, Virendra
5 Citations
We propose an analytic perturbative approach for the determination of the FeigenbaumCvitanović function and the universal parameterα occurring in the Feigenbaum scenario of period doubling for approach to chaotic behaviour. We apply the method to the caseZ=2 whereZ is the order of the unique local maximum of the nonlinear map. Our third order approximation givesα=2.5000 as compared to “exact” numerical valueα=2.5029 ... We also obtain a reasonably accurate value of the FeigenbaumCvitanović function.
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By
Mehta, Mitaxi P; Sitaram, B R
In this communication, we report the results of the application of time dependent perturbation theory to a nonintegrable Hamiltonian which is a perturbation on a Hamiltonian with nonconstant frequencies. The theory provides good time dependent local constants of motion and also gives good approximation for mapping of solutions for a time limit determined by the nearest singularity in complexε plane for fixed real time and the order of calculation.
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By
Sikri, A. K.; Narchal, M. L.
The quantum motion of a periodically twosided kicked free particle is studied under various boundary conditions. The quasienergies, quasistates and the energy of the system are determined exactly. It is found that the energy of the system recurs irrespective of boundary conditions whereas the wave function shows recurrence only for a completely bound particle.
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By
Batra, Sangeeta; Varma, V S
2 Citations
We study discrete nonlinear maps in which the control parameter is itself “modulated” by another discrete nonlinear map. We show that for a certain class of such maps, which includes for example the logistic map, the periodicity of the modulated signal is either one, independent of the periodicity of the modulating signal, or its periodicity is an integral multiple of the periodicity of the modulating signal or it is chaotic.
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By
Parikh, Jitendra C; Pratap, R
4 Citations
A model of electrical activity of human brain considered as a complex dynamical system is given based on the EEG time series. The model fits the data remarkably well. The predictive ability of the model is limited to a few time steps as expected for a chaotic time series.
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By
Mehta, Mitaxi P; Sitaram, B R
1 Citations
In this communication, we report the results of the application of timedependent perturbation theory to the HenonHeiles system. We show that the predictions of the perturbation theory hold good for short times, and try to explain the increase of error in the predicted results with the increase in energy.
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By
Valsamma, K M; Joseph, K Babu; Ambika, G
We present an analytic perturbative method for calculatingf(α) and the generalized dimensionD_{q} 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.
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By
Rajasekar, S
2 Citations
The influence of timedependent periodic optical drive in the FabryPerot interferometer system has been investigated using a theoretical model equation. A variety of features such as different routes to chaos, multiperiodic oscillations, coexistence of multiple attractors and modelocking with devil’s staircase are found to occur for a certain range of parametric values.
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By
Sikri, A K; Narchal, M L
The problem of a free electron periodically kicked by a magnetic field has been solved. The system shows a transition from quantum recurrence to instability at ωT=2 where ω is the Larmor frequency andT is the period of the kick. The existence of recurrent behaviour amounts to the confinement of the electron by magnetic kicking. Since the theory holds for all types of charged particles, it has many practical applications.
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