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

Fish habitats and species assemblage in the selected rivers of Kerala and investigation on life history traits of Puntius carnaticus(Jerdon,1849)

This thesis entitled Fish habitats and species assemblage in the selected rivers of kerala and investigation on life history traits of puntius carnaticus (JERDON,1849). Ecology is a new and exceedingly complex field of study, even though its concept was recognized by the Apostles in their use of the phrase ‘all flesh is grass.central role to play both in order to understand better the biodiversity phenomenon and to be able to draw up clear guidelines for careful resource management. In a review by WWF, IUCN and UNEP on the ways of conserving genetic diversity of freshwater fish it was recommended that the best way to conserve species diversity is to conserve habitat.The habitat studies in freshwater ecosystems are very essential for the proper understanding and management of human impact on fish diversity, to study the relationship between habitat variables and fish species assemblage structure, quantification of ecosystem degradation, habitat quality and biotic integrity of the ecosystems, development of habitat suitability index (I-ISI) models and classification of river reaches based on their physico-chemical properties. Therefore in the present study an attempt was made to assess the biodiversity potential and the relationship between habitat variables and fish species assemblage structure in six major river systems of Kerala which would be very useful in impressing upon the seriousness of habitat degradIn the present study, in Kabbini river system 15 locations encompassing between 721 946m above MSL were surveyed.ation and biotic devastation undergone in the major river systems of Kerala.During the present study the Habitat Quality Score (HQ) developed by the Ohio EPA was applied for the first time in India.The result of the present study revealed that, among various variables analysed, altitude has a very significant influence in deciding the fish diversity in six major river systems of Kerala. The fish diversity studied on the basis of Shanon-Weiner and Simpson diversity indices revealed that even though some minor variations occur with the suitability and complexity of habitats, the altitude showed inverse relationship with fish diversity.The present study revealed that the National Policy on the interlinking of rivers would permanently alter the HSI indices of the above mentioned fish species, which are now solely protected by the individuality of the rivers where their limited occurrence was notice.