Exploring diverse trajectory patterns in nonlinear dynamic systems

Abstract

Describing the dynamical properties of explored systems, one finds the need to distinguish between various types of trajectories. The nature of trajectories is often split into regular and irregular, which will be shown in this paper as too crude. Hence, the main aim of this paper is to give a classification of trajectories reflecting persistence, regularity, chaos, intermittency, and transiency. To depict such phenomena, classical examples from discrete (the Rulkov map) and continuous (the Lorenz system) dynamical systems are applied. In these cases, the maximal Lyapunov exponent, the 0-1 test for chaos, the bifurcation diagram, and the Fourier analysis are applied, and these dynamics characteristics are confronted with trajectory types.