Algorithmic detection of type-I intermittency

Abstract

The goal of the thesis is to develop an algorithm for detection of type-I intermittency in discrete dynamical systems. Intermittency in a dynamical system is a phenomenon where the state of the system alternates between being seemingly stable and chaotic. The focus of the thesis is on the type-I intermittency which is associated with saddle-node bifurcations. First, the theory of discrete dynamical systems and of type-I intermittency is introduced. Furthermore, the importance of detection of type-I intermittency is explained. By combining several algorithms of various authors, the detection is achieved for the Logistic map. The results of the detection are presented graphically through colorization of a bifurcation diagram. Lastly, the implementation in Julia programming language is mentioned.