ABSTRACT
This chapter conducts a broad survey of some of the major issues of a dynamical system. As is widely recognized, a modern treatment of classical mechanics is incomplete without an insight from the standard ideas and techniques of dynamical systems. Among them are essentially the theory of stability, limit cycles and bifurcations. The chapter first provides the definitions of various concepts that frequently appear in dynamical systems. It places a greater emphasis on the linear systems and discusses how the process of linearization can be carried out for different classes of nonlinear systems under certain suitable conditions. The chapter discusses the Lotka–Volterra model which is a popular model for prey-predator species. It considers the stability of solutions and the role of the Lyapunov function. The concept of limit cycles was explained by means of models including the one of Van der Pol oscillator. Several aspects of bifurcations were treated through model examples.
