EXPLAINING BIFURCATIONS

Abstract. This paper will introduce the topic of dynamical systems with both discrete and continuous time variables. Fixed points will be discussed, along with their properties such as stability or topological type. The paper will continue on to define the concept of hyperbolicity and its relevance in determining the structural stability of the system. It will conclude with a definition of a bifurcation as well as a brief description of bifurcation theory and its applications. 1