V M Nandakumaran
Articles written in Pramana – Journal of Physics
Volume 29 Issue 6 December 1987 pp 533-542 Statistical Physics
Bifurcation structure and Lyapunov exponents of a modulated logistic map
K P Harikrishnan V M Nandakumaran
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.
Volume 33 Issue 6 December 1989 pp 697-704 Condensed Matter Physics
Solitons and their resonances on two-dimensional superfluid films
The dynamics of saturated two-dimensional superfluid4He films is shown to be governed by the Kadomtsev-Petviashvili equation with negative dispersion. It is established that the phenomena of soliton resonance could be observed in such films. Under the lowest order nonlinearity, such resonance would happen only if two dimensional effects are taken into account. The amplitude and velocity of the resonant soliton are obtained.
Volume 43 Issue 6 December 1994 pp 421-429
Scaling relations in the lyapunov exponents of one dimensional maps
P R Krishnan Nair V M Nandakumaran G Ambika
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.
Volume 47 Issue 5 November 1996 pp 339-345
Dynamics of the logistic map under discrete parametric perturbation
P P Saratchandran V M Nandakumaran G Ambika
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.
Volume 48 Issue 1 January 1997 pp 99-108 Mathematical Aspects Of Dynamical Systems
Chaos in modulated logistic systems
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.
Volume 54 Issue 3 March 2000 pp 393-402 Research Articles
Dynamics of two coupled chaotic multimode Nd:YAG lasers with intracavity frequency doubling crystal
Thomas Kuruvilla V M Nandakumaran
The effect of coupling two chaotic Nd:YAG lasers with intracavity KTP crystal for frequency doubling is numerically studied for the case of the laser operating in three longitudinal modes. It is seen that the system goes from chaotic to periodic and then to steady state as the coupling constant is increased. The intensity time series and phase diagrams are drawn and the Lyapunov characteristic exponent is calculated to characterize the chaotic and periodic regions.
Volume 97, 2023
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