Some applications of Delay Differential Equation

Abstract

The present thesis entitled Some applications of delay differential equations is an outcome of my work over the last five years with an aim to submit it to the Fakir Mohan University, Balasore in partial fulfillment of the requirements for the award of the degree of Doctor of Philosophy in Mathematics. The primary object of this thesis is to study the delay differential models used in mathematical biology, population dynamics and stability of delay differential equations using different methods. We have collected here most of the results subject to availability and presented them in order of their publication or relation with previous results. newlineChapter-1, is an introductory which gives a brief history and development of delay differential equations. newlineChapter-2, contains a literature review regarding DDEs. It also contains Research objective and Research methodology. newlineChapter-3, contains basic definitions of delay differential equations which are needed throughout the work. newlineChapter-4, introduces comparative study of DDEs and ODEs have been reflected and how the DDEs are solved by converting it to ODEs. newlineChapter-5, is an introduction for solving delay differential equations using market equilibrium. newlineChapter-6, provides the exploitation of a single species system with stage structure and harvesting, where harvesting effort is constant and we established global stability of the equilibrium under some contains. newlineChapter-7, generalizes a proposed mathematical model and analyzed to study the dynamics of a predator-prey system due to time lags for conversion of biomass. newlineChapter-8, concerns the stability analysis of first order delay differential equations, with constant coefficients. newlineChapter-9, provides an algebraic approach to study the stability of second order linear delay differential equation which is the extension of first order linear delay differential equations. newline newline