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.
Bindu M, Krishna; Manu P, John; Nandakumaran, V M(Indian Academy of Sciences, February , 2010)
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Abstract:
Chaotic synchronization of two directly modulated semiconductor lasers with
negative delayed optoelectronic feedback is investigated and this scheme is found to be
useful for e±cient bidirectional communication between the lasers. A symmetric bidirec-
tional coupling is identified as a suitable method for isochronal synchronization of such
lasers. The optimum values of coupling and feedback strength that can provide maxi-
mum quality of synchronization are identified. This method is successfully employed for
encoding/decoding both analog and digital messages. The importance of a symmetric
coupling is demonstrated by studying the variation of decoding efficiency with respect to
asymmetric coupling.
Harikrishnan, K P; Nandakumaran, V M(Pramana, December , 1987)
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Abstract:
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.
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.
Nandakumaran, V M; Bindu M, Krishna; Manu P, John(Cochin University of Science & Technology, 2004)
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Abstract:
Chaotic dynamics of directly modulated semiconductor lasers have been
studied extensively over the last two decades because of their application in secure
optical communication. However, chaos is generally suppressed in such systems when
the nonlinear gain reduction factor is above 0.01 which is very much smaller than
the reported values in semiconductors like InGaAsP. In this paper we show that by
giving an optoelectronic feedback with appropriate delay one can increase the range
of the values of the gain reduction factor for which chaos can be observed. Numerical
studies show that negative feedback is more efficient in producing chaotic dynamics.
Rajesh, S; Nandakumaran, V M(Elsevier, January , 2006)
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Abstract:
We show numerically that direct delayed optoelectronic feedback can suppress hysteresis and bistability in a directly modulated semiconductor laser. The simulation of a laser with feedback is performed for a considerable range of feedback strengths and delays and the corresponding values for the areas of the hysteresis loops are calculated. It is shown that the hysteresis loop completely vanishes for certain combinations of these parameters. The regimes for the disappearance of bistability are classified globally. Different dynamical states of the laser are characterized using bifurcation diagrams and time series plots.
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.
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.
Thomas, Kuruvilla; Nandakumaran, V M(Indian Academy of Sciences, March , 2000)
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Abstract:
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.
Manu P, John; Jijo, P U; Nandakumaran, V M(Indian Academy of Sciences, March , 2009)
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Abstract:
We study the effect of parameter fluctuations and the resultant multiplicative
noise on the synchronization of coupled chaotic systems. We introduce a new quantity,
the fluctuation rate Ф as the number of perturbations occurring to the parameter in unit
time. It is shown that ϕ is the most significant quantity that determines the quality of
synchronization. It is found that parameter fluctuations with high fluctuation rates do not
destroy synchronization, irrespective of the statistical features of the fluctuations. We also
present a quasi-analytic explanation to the relation between ϕ and the error in synchrony.
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.
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.
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.