Stability of Systems of Differential Equations and Biological Applications

ABSTRACT: In this thesis, we deal with systems of ordinary differential equations and discuss the stability properties of their solutions. We classify equilibrium points of linear systems with respect to their type and stability and discuss the methods for investigating the stability properties of nonlinear systems. Existence of periodic solutions which plays an important role in stability theory is also discussed. In addition, some important ecological applications, such as Lotka-Volterra predator-prey model, competition model and nutrient-prey-predator model with intratrophic predation, modeled by the systems of differential equations are also considered. Recent results obtained for these applications are also included. Keywords: Stability, Periodic solution, Predator-prey model, Intratrophic predation. ……………………………………………………………………………………………………………………………………………………………………………………………………………………