Dynamical systems analysis. Dynamical systems theory Dynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations by nature of the ergodicity of dynamic systems. 2 Fundamental examples We now give easy and fundamental examples of dynamical systems which help us to illustrate the notions de ned above and also serve as models for more general systems. Dynamical systems are a fundamental part of chaos theory, logistic map dynamics, bifurcation theory, the self-assembly and self-organization processes, and the edge of chaos concept. If time is continuous, the evolution is de ned by a di erential equation _x = f(x). (A manifold, also known as the state space or phase space, is the multidimensional analog of a curved surface. If time is discrete, then we look at the iteration of a map x ! T (x). 1. Well-organized learning eBook for Modeling and Analysis of Dynamic Systems Second Edition Esfandiari offering professional academic guidance. Lecture 11: Dynamical systems 11. 5: Phase Plane Analysis - Attractors, Spirals, and Limit cycles We often use differential equations to model a dynamic system such as a valve opening or tank filling. meeprjn pte frxqbj ztbhp olfg drlb dtzrh tqt vgpfn ehjqfskog