Krishnan Nair, P R; Nandakumaran, V M(Springer, October , 1998)
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Abstract:
We present the analytical investigations on a logistic map with a discontinuity at the
centre. An explanation for the bifurcation phenomenon in discontinuous systems is presented. We
establish that whenever the elements of an n-cycle (n > 1) approach the discontinuities of the nth
iterate of the map, a bifurcation other than the usual period-doubling one takes place. The periods of
the cycles decrease in an arithmetic progression, as the control parameter is varied. The system also
shows the presence of multiple attractors. Our results are verified by numerical experiments as well.
Amritkar, R E; Gade, P M; Gangal, A D; Nandkumaran, V M(The American Physical Society, September , 1991)
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Abstract:
We consider the stability properties of spatial and temporal periodic orbits of one-dimensional coupled-map lattices. The stability matrices for them are of the block-circulant form. This helps us to reduce the problem of stability of spatially periodic orbits to the smaller orbits corresponding to the building blocks of spatial periodicity, enabling us to obtain the conditions for stability in terms of those for smaller orbits.
Thomas, Kuruvilla; Nandakumaran, V M(Elsevier, April , 1999)
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Abstract:
The effect of coupling on two high frequency modulated semiconductor lasers is numerically studied. The phase diagrams and bifurcatio.n diagrams are drawn. As the coupling constant is increased the system goes from chaotic to periodic behavior through a reverse period doubling sequence. The Lyapunov exponent is calculated to characterize chaotic and periodic regions.
This paper is a review of the work done on the dynamics of modulated logistic systems.
Three different problems are treated, viz, the modulated logistic map, the parametrically perturbed
logistic map and the combination map obtained by combining two maps of the quadratic family.
Many of the interesting features displayed by these systems are discussed.
Saratchandran, P P; Nandakumaran, V M; Ambika, G(Springer, November , 1996)
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Abstract:
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.
Suresh V, Vettoor; Nandakumaran, V M(Physica C,Elsevier Science, 1992)
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Abstract:
The density of states and the low temperature specific heat of higb-Tc superconductors are calculated in a functional integral formalism using the slave boson technique. The manybody calculation in a saddle point approximation shows that the Iow energy
sector is dominated by 3 single band. The calculated values of density of states are in good agreement with experimental results.
Kriashnan Nair, P R; Nandakumaran, V M; Ambika, G(Pramana, December , 1994)
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Abstract:
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.
Thomas, Kuruvilla; Nandakumaran, V M(American Institute of Physics, March , 1999)
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Abstract:
We have numerically studied the behavior of a two-mode Nd-YAG laser with an intracavity KTP crystal. It is found that when the parameter, which is a measure of the relative orientations of the KTP crystal with respect to the Nd-YAG crystal, is varied continuously, the output intensity fluctuations change from chaotic to stable behavior through a sequence of reverse period doubling bifurcations. The graph of the intensity in the X-polarized mode against that in the Y-polarized mode shows a complex pattern in the chaotic regime. The Lyapunov exponent is calculated for the chaotic and periodic regions.
Ambika, G; Nandakumaran, V M; Babu Joseph, K(World Scientific Publishing Company, 1991)
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Abstract:
We consider a resistively shunted Josephson junction with a resistance that depends inversely on voltage. It is shown that such a junction in the underdamped case can give rise to extremely long-lived metastable states even in the absence of external noise. We investigate numerically this metastable state and its transition to a chaotic state. The junction voltages corresponding to these states are studied.
Suresh V, Vettoor; Nandakumaran, V M(World Scientific Publishing Company, 1990)
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Abstract:
Electron-phonon interaction is considered within the framework of the fluctuating
valence of Cu atoms. Anderson's lattice Hamiltonian is suitably modified to take this into
account. Using Green's function technique tbe possible quasiparticle excitations' are
determined. The quantity 2delta k(O)/ kB Tc is calculated for Tc= 40 K. The calculated values
are in good agreement with the experimental results.