Dynamics of Biological Species: Some Mathematical Models

Abstract

it helps to describe the logical consequence of assumptions data and the described knowledge of processes and iii it can explore the behaviour of complex system more reliably than mental model provided the assumptions are wellunderstood Keeping the above aspects in mind in this thesis we propose and analyze some mathematical models to study the dynamics of some biological species Various aspect of interaction of biological populations with crowding effects various types of nonlinear harvesting rate of renewable resources and different types of nonlinear treatment rates of infected populations are considered in the formulation of the models These models have been analyzed using the stability theory of Ordinary Differential Equations and finally computer simulations have been carried out to validate the qualitative analysis The whole work is discussed in seven separate chapters whose abstracts are given below In Chapter 1 a brief introduction with literature has been presented to provide a background required for the upcoming chapters Further an overview of mathematical tools for establishing local and global stability of the steady states of dynamical models which has been used in the sub sequent chapters is also given In Chapter 2 a dynamical model has been proposed and analyzed to study the effect of population on resource biomass by taking into account the crowing effect The resource biomass and population both are growing logistically The population partially depends on the resource and utilizes the resource for its own growth and development The population grow both linearly and nonlinearly with the presence of the resource The resource biomass which has commercial importance is harvested according to catchperunit effort hypothesis and the harvesting effort is a control variable newlineThe existence of equilibria and stability analysis have been discussed with the help of stability theory of ordinary differential equations It has been shown that the positive equilibrium whenever it exists is always locally asymp