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Harikrishnan, K P; Nandakumaran, V M (Elsevier, December 25, 1989)[+][-]
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. URI: http://dyuthi.cusat.ac.in/purl/2567 ## Files in this item: 1

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Bindu M, Krishna; Manu P, John; Nandakumaran, V M (Indian Academy of Sciences, February , 2010)[+][-]
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. URI: http://dyuthi.cusat.ac.in/purl/2525 ## Files in this item: 1

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Harikrishnan, K P; Nandakumaran, V M (Pramana, December , 1987)[+][-]
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. URI: http://dyuthi.cusat.ac.in/purl/2562 ## Files in this item: 1

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Nandakumaran, V M (Springer, January , 1997)[+][-]
Abstract: 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. URI: http://dyuthi.cusat.ac.in/purl/2536 ## Files in this item: 1

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Nandakumaran, V M; Bindu M, Krishna; Manu P, John (Cochin University of Science & Technology, 2004)[+][-]
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. URI: http://dyuthi.cusat.ac.in/purl/2539 ## Files in this item: 1

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Rajesh, S; Nandakumaran, V M (Elsevier, January , 2006)[+][-]
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. URI: http://dyuthi.cusat.ac.in/purl/2531 ## Files in this item: 1

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Suresh V, Vettoor; Nandakumaran, V M (Physica C,Elsevier Science, 1992)[+][-]
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. URI: http://dyuthi.cusat.ac.in/purl/2563 ## Files in this item: 1

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Sreekumar, J; Nandakumaran, V M (Department of Physics, 1990)[+][-]
URI: http://dyuthi.cusat.ac.in/purl/1716 ## Files in this item: 1

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Saratchandran, P P; Nandakumaran, V M; Ambika, G (Springer, November , 1996)[+][-]
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. URI: http://dyuthi.cusat.ac.in/purl/2558 ## Files in this item: 1

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Thomas, Kuruvilla; Nandakumaran, V M (Indian Academy of Sciences, March , 2000)[+][-]
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. URI: http://dyuthi.cusat.ac.in/purl/2532 ## Files in this item: 1

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Manu P, John; Jijo, P U; Nandakumaran, V M (Indian Academy of Sciences, March , 2009)[+][-]
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. URI: http://dyuthi.cusat.ac.in/purl/2527 ## Files in this item: 1

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Suresh V, Vettoor; Nandakumaran, V M (World Scientific Publishing Company, 1990)[+][-]
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. URI: http://dyuthi.cusat.ac.in/purl/2565 ## Files in this item: 1

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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. URI: http://dyuthi.cusat.ac.in/purl/2569 ## Files in this item: 1

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Krishnan Nair, P R; Nandakumaran, V M (Springer, October , 1998)[+][-]
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. URI: http://dyuthi.cusat.ac.in/purl/2535 ## Files in this item: 1

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Ambika, G; Nandakumaran, V M (Current Science, January 25, 1990)[+][-]
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. URI: http://dyuthi.cusat.ac.in/purl/2707 ## Files in this item: 1

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Parvathi, M R; Bindu M, Krishna; Rajesh, S; Manu P, John; Nandakumaran, V M (Elsevier, October , 2009)[+][-]
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. URI: http://dyuthi.cusat.ac.in/purl/2528 ## Files in this item: 1

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Nandakumaran, V M (IOP, 1985)[+][-]
Abstract: 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. URI: http://dyuthi.cusat.ac.in/purl/2538 ## Files in this item: 1

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Krishnan Nair, P R; Nandakumaran, V M (Cochin University of Science and Technology, October , 1999)[+][-]
Abstract: This thesis is a study of discrete nonlinear systems represented by one dimensional mappings.As one dimensional interative maps represent Poincarre sections of higher dimensional flows,they offer a convenient means to understand the dynamical evolution of many physical systems.It highlighting the basic ideas of deterministic chaos.Qualitative and quantitative measures for the detection and characterization of chaos in nonlinear systems are discussed.Some simple mathematical models exhibiting chaos are presented.The bifurcation scenario and the possible routes to chaos are explained.It present the results of the numerical computational of the Lyapunov exponents (λ) of one dimensional maps.This thesis focuses on the results obtained by our investigations on combinations maps,scaling behaviour of the Lyapunov characteristic exponents of one dimensional maps and the nature of bifurcations in a discontinous logistic map.It gives a review of the major routes to chaos in dissipative systems,namely, Period-doubling ,Intermittency and Crises.This study gives a theoretical understanding of the route to chaos in discontinous systems.A detailed analysis of the dynamics of a discontinous logistic map is carried out, both analytically and numerically ,to understand the route it follows to chaos.The present analysis deals only with the case of the discontinuity parameter applied to the right half of the interval of mapping.A detailed analysis for the n –furcations of various periodicities can be made and a more general theory for the map with discontinuities applied at different positions can be on a similar footing URI: http://dyuthi.cusat.ac.in/purl/1012 ## Files in this item: 1

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Ambika, G; Nandakumaran, V M; Babu Joseph, K (World Scientific Publishing Company, 1991)[+][-]
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. URI: http://dyuthi.cusat.ac.in/purl/2564 ## Files in this item: 1

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Bindu M, Krishna; Manu P, John; Nandakumaran, V M (Elsevier, April , 2010)[+][-]
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. URI: http://dyuthi.cusat.ac.in/purl/2526 ## Files in this item: 1

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