Ambika, G; Nandakumaran, V M(Current Science, January 25, 1990)
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Abstract:
We discuss how the presence of frustration brings about
irregular behaviour in a pendulum with nonlinear
dissipation. Here frustration arises owing to
particular choice of the dissipation. A preliminary
numerical analysis is presented which indicates the transition
to chaos at low frequencies of the driving force.
Harikrishnan, K P; Nandakumaran, V M(Elsevier, December 7, 1987)
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Abstract:
We study the period-doubling bifurcations to chaos in a logistic map with a nonlinearly modulated parameter and show that the bifurcation structure is modified significantly. Using the renormalisation method due to Derrida et al. we establish the universal behaviour of the system at the onset of chaos.
The role of acoustic plasmons in the recently discovered high Tc superconductors
is discussed. It is shown that the exchange of acoustic plasmons together with the
usual phonon exchange between electrons can give rise to a Tc - 100 K.
Harikrishnan, K P; Nandakumaran, V M(Elsevier, November 21, 1988)
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Abstract:
We analyse numerically the bifurcation structure of a two-dimensional noninvertible map and show that different periodic cycles are arranged in it exactly in the same order as in the case of the logistic map. We also show that this map satisfies the general criteria for the existence of Sarkovskii ordering, which supports our numerical result. Incidently, this is the first report of the existence of Sarkovskii ordering in a two-dimensional map.
Sreekumar, J; Nandakumaran, V M(Springer, December , 1989)
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Abstract:
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.
Harikrishnan, K P; Nandakumaran, V M(Elsevier, December 7, 1987)
[+]
[-]
Abstract:
We study the period-doubling bifurcations to chaos in a logistic map with a nonlinearly modulated parameter and show that the bifurcation structure is modified significantly. Using the renormalisation method due to Derrida et al. we establish the universal behaviour of the system at the onset of chaos.
The role of acoustic plasmons in the recently discovered high Tc superconductors
is discussed. It is shown that the exchange of acoustic plasmons together with the
usual phonon exchange between electrons can give rise to a Tc - 100 K.
Harikrishnan, K P; Nandakumaran, V M(Elsevier, November 21, 1988)
[+]
[-]
Abstract:
We analyse numerically the bifurcation structure of a two-dimensional noninvertible map and show that different periodic cycles are arranged in it exactly in the same order as in the case of the logistic map. We also show that this map satisfies the general criteria for the existence of Sarkovskii ordering, which supports our numerical result. Incidently, this is the first report of the existence of Sarkovskii ordering in a two-dimensional map.
Sreekumar, J; Nandakumaran, V M(Springer, December , 1989)
[+]
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Abstract:
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.
Harikrishnan, K P; Nandakumaran, V M(Elsevier, December 25, 1989)
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Abstract:
This is a sequel to our earlier work on the modulated logistic map. Here, we first show that the map comes under the universality class of Feigenbaum. We then give evidence for the fact that our model can generate strange attractors in the unit square for an uncountable number of parameter values in the range μ∞<μ<1. Numerical plots of the attractor for several values of μ are given and the self-similar structure is explicity shown in one case. The fractal and information dimensions of the attractors for many values of μ are shown to be greater than one and the variation in their structure is analysed using the two Lyapunov exponents of the system. Our results suggest that the map can be considered as an analogue of the logistic map in two dimensions and may be useful in describing certain higher dimensional chaotic phenomena.