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.
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.
Parvathi, M R; Bindu M, Krishna; Rajesh, S; Manu P, John; Nandakumaran, V M(Elsevier, October , 2009)
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Abstract:
Dynamics of Nd:YAG laser with intracavity KTP crystal operating in two parallel polarized modes is investigated analytically and numerically. System equilibrium points were found out and the stability of each of them was checked using Routh–Hurwitz criteria and also by calculating the eigen values of the Jacobian. It is found that the system possesses three equilibrium points for (Ij, Gj), where j = 1, 2. One of these equilibrium points undergoes Hopf bifurcation in output dynamics as the control parameter is increased. The other two remain unstable throughout the entire region of the parameter space. Our numerical analysis of the Hopf bifurcation phenomena is found to be in good agreement with the analytical results. Nature of energy transfer between the two modes is also studied numerically.
For the discrete-time quadratic map xt+1=4xt(1-xt) the evolution equation for a class of non-uniform initial densities is obtained. It is shown that in the t to infinity limit all of them approach the invariant density for the map.
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.
Bindu M, Krishna; Manu P, John; Nandakumaran, V M(Elsevier, April , 2010)
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Abstract:
Isochronal synchronisation between the elements of an array of three mutually coupled directly modulated semiconductor lasers is utilized for the purpose of simultaneous bidirectional secure communication. Chaotic synchronisation is achieved by adding the coupling signal to the self feedback signal provided to each element of the array. A symmetric coupling is effective in inducing synchronisation between the elements of the array. This coupling scheme provides a direct link between every pair of elements thus making the method suitable for simultaneous bidirectional communication between them. Both analog and digital messages are successfully encrypted and decrypted simultaneously by each element of the array.
Bindu, V; Nandakumaran, V M(Elsevier, December 11, 2000)
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Abstract:
Results of a numerical study of synchronisation of two directly modulated semiconductor lasers, using bi-directional coupling, are presented. The effect of stepwise increase in the coupling strength (C) on the synchronisation of the chaotic outputs of two such lasers is studied, with the help of parameter space plots, synchronisation error plots, phase diagrams and time series outputs. Numerical results indicate that as C increases, the system achieves synchronisation as well as stability together with an increase in the output power. The stability of the synchronised states is checked by applying a perturbation to the system after it becomes synchronised and then noting the time it takes to regain synchronisation. For lower values of C the system does not regain synchronisation. But, with higher values synchronisation is regained within a very short time.
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.
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.
Bindhu M, Krishna; Manu P, John; Nandakumaran, V M(Indian Academy of Sciences, December , 2008)
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Abstract:
The chaotic dynamics of directly modulated semiconductor lasers with delayed optoelectronic feedback is studied numerically. The effects of positive and negative delayed optoelectronic feedback in producing chaotic outputs from such lasers with nonlinear gain reduction in its optimum value range is investigated using bifurcation diagrams. The results are confirmed by calculating the Lyapunov exponents. A negative delayed optoelectronic feedback configuration is found to be more effective in inducing chaotic dynamics to such systems with nonlinear gain reduction factor in the practical value range.
A dynamical system with a damping that is quadratic in velocity is converted into the Hamiltonian format using a nonlinear transformation. Its quantum mechanical behaviour is then analysed by invoking the Gaussian effective potential technique. The method is worked out explicitly for the Duffing oscillator potential.
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.
Sreekumar, J; Nandakumaran, V M(Physics Letters, October 21, 1985)
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Abstract:
The phenomenon of two-soliton resonances of the Kadomtsev-Petviashvilli equation for the superfluid surface density fluctuation in He films is studied. The velocity of the resonant soliton is obtained.
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.
Nandakumaran, V M; V P N Nampoori; Radhakrishnan, P; Girijavallabhan, C P; Dann, V J; Mathew, M V(Plasma Science and Technology, August , 2007)
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Abstract:
Optical emission from TiO2 plasma, generated by a nanosecond laser is spectroscopically
analysed. The main chemical species are identified and the spatio-temporal distribution of
the plasma parameters such as electron temperature and density are characterized based on the
study of spectral distribution of the line intensities and their broadening characteristics. The parameters
of laser induced plasma vary quickly owing to its expansion at low background pressure
and the possible deviations from local thermodynamic equilibrium conditions are tested to show
its validity.
Amritkar, R E; Gade, P M; Gangal, A D; Nandakumaran, 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.
Parvathi, M R; Bindu M, Krishna; Rajesh, S; Manu P, John; Nandakumaran, V M(Elsevier, December , 2008)
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Abstract:
In this Letter we numerically investigate the dynamics of a system of two coupled chaotic multimode Nd:YAG lasers with two mode and three mode outputs. Unidirectional and bidirectional coupling schemes are adopted; intensity time series plots, phase space plots and synchronization plots are used for studying the dynamics. Quality of synchronization is measured using correlation index plots. It is found that for laser with two mode output bidirectional direct coupling scheme is found to be effective in achieving complete synchronization, control of chaos and amplification in output intensity. For laser with three mode output, bidirectional difference coupling scheme gives much better chaotic synchronization as compared to unidirectional difference coupling but at the cost of higher coupling strength. We also conclude that the coupling scheme and system properties play an important role in determining the type of synchronization exhibited by the system.
Sreekumar, J; Nandakumaran, V M(World Scientific Publishing Company, 1990)
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Abstract:
Large amplitude local density fluctuations in a thin superfluid He film is considered. It is shown that these large amplitude fluctuations travel and behave like "quasi-solitons" under collision, even when the full nonlinearity arising from the Van der Waals potential is taken into account.
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.