Bifurcation structure and Lyapunov exponents of a modulated logistic map

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.

Investigations on the Dynamics of Combination Maps and the Analysis of Bifurcation in a Discontinuous Logistic Map

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

Numerical study of reverse period doubling route from chaos to stability in a two-mode intracavity doubled Nd-YAG laser

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.

Metglas thin film based magnetostrictive transducers for use in long period fibre grating sensors

Metallic glass alloy Metglas 2826 MB based amorphous magnetic thin films were fabricated by the thermal evaporation technique. Transmission electron micrographs and electron diffraction pattern showed the amorphous nature of the films. Composition of the films was analyzed employing x-ray photoelectron spectroscopy and energy dispersive x-ray spectroscopy techniques. The film was integrated to a long period fibre grating. It was observed that the resonance wavelength of the fibre grating decreased with an increase in the magnetic field. Change in the resonance wavelength was minimal at higher magnetic fields. Field dependent magnetostriction values revealed the potential application of these films in magnetostrictive sensor devices

Nonlinear Dynamics of Nd:YAG lasers: Hopf bifurcation, Multistability and Chaotic Synchronization

In this thesis we have presented some aspects of the nonlinear dynamics of Nd:YAG lasers including synchronization, Hopf bifurcation, chaos control and delay induced multistability.We have chosen diode pumped Nd:YAG laser with intracavity KTP crystal operating with two mode and three mode output as our model system.Different types of orientation for the laser cavity modes were considered to carry out the studies. For laser operating with two mode output we have chosen the modes as having parallel polarization and perpendicular polarization. For laser having three mode output, we have chosen them as two modes polarized parallel to each other while the third mode polarized orthogonal to them.

Impact of Monetary Policy on Indian Economy in the Post-Reform Period

The present study was an attempt to analyze systematically the techniques of monetary control measures with its relevance and changing importance and to find out their effectiveness in the Indian context especially to achieve the thriving objectives of price stability and economic growth.There is definite and remarkable economic impact of monetary policy on Indian economy in the post-reform period. The importance of monetary policy has been increasing year after year. Its role is very relevant in attaining monetary objectives, especially in managing price stability and achieving economic growth. Along that, the use and importance of monetary weapons like Bank rate, CRR, SLR, Repo rate and Reverse Rate have increased over the years. Repo and Reverse Repo rates are the most frequently used monetary techniques in recent years. The rates are varied mainly for curtailing inflation and absorb the excess liquidity and hence to maintain price stability in the economy. Thus, this short-time objective of price stability is more successful on Indian economy rather than other long-term objectives of development.Monetary policy rules can be active or passive. The passive rule is to keep the money supply constant, which is reminiscent of Milton Friedman’s money growth rule. The second, called a price stabilization rule, is to change the money supply in response to changes in aggregate supply or demand to keep the price level constant. The idea of an active rule is to keep the price level and hence inflation in check. In India, this rule dominates our monetary policy. A stable growth is healthy growth.

Long period gratings in multimode optical fibers: application in chemical sensing

We propose and demonstrate a new technique for evanescent wave chemical sensing by writing long period gratings in a bare multimode plastic clad silica fiber. The sensing length of the present sensor is only 10 mm, but is as sensitive as a conventional unclad evanescent wave sensor having about 100 mm sensing length. The minimum measurable concentration of the sensor reported here is 10 nmol/l and the operating range is more than 4 orders of magnitude. Moreover, the detection is carried out in two independent detection configurations viz., bright field detection scheme that detects the core-mode power and dark field detection scheme that detects the cladding mode power. The use of such a double detection scheme definitely enhances the reliability and accuracy of the results. Furthermore, the cladding of the present fiber need not be removed as done in conventional evanescent wave fiber sensors.

Hopf bifurcation in parallel polarized Nd:YAG laser

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.

Suppression of chaos through reverse period doubling in coupled directly modulated semiconductor lasers

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.

Existence of multiple attractors and the nature of bifurcations in a discontinuous logistic map

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.