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

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.

Studies on some generalizations of line graph and the power domination problem in graphs

Department of Mathematics, Cochin University of Science and Technology

Optimization of Process Parameters for the Extraction of Gelatin from the Skin of Freshwater Fish and the Evaluation of Physical anal Chemical Characteristics

Faculty of Marine Sciences,Cochin University of Science and Technology

Kinetic Studies of Purified malate Dehydrogenase in Liver of Streptozotocindiabetic Rats and the Effect of Leaf Extract of Aegle Marmelose (L.) Correa ex Roxb

The functional basis of diabetes-mellitus to a certain extent, can be elucidated by studying diabetes-induced changes in metabolic enzymes. Malate dehydrogenase (MDH), is an enzyme directly involved in glucose metabolism. The kinetic parameters of MDH and its purified cytosolic isozyme, S-MDH, have been studied in the liver of streptozotocin- diabetic rats; also the potential of the leaf extract of A. marmelose as an was investigated. The Km of the liver enzyme increased significantly, in both crude and purified preparations in the diabetic state when compared to Lhe respective controls. Insulin as well as leaf- •extract treatment of the diabetic rats brought about a reversal of K. values to near normal. Vmax of purified S-MDH was significantly higher in the diabetic state when compared to the control. Insulin and leaf extract treatment did not reverse this change. Since MDH is an important enzyme in glucose metabolism, the variation in its quantitative and qualitative nature may contribute to the pathological status of diabetes. The fact that leaf extract of A. marmelose was found to be as effective as insulin in restoration of blood glucose and body weight to normal levels, the use of A. marmelose as potential hypoglycemic agent is suggested.