An Introduction to Chaotic Dynamical Systems

  title={An Introduction to Chaotic Dynamical Systems},
  author={Robert L. Devaney},
Part One: One-Dimensional Dynamics Examples of Dynamical Systems Preliminaries from Calculus Elementary Definitions Hyperbolicity An example: the quadratic family An Example: the Quadratic Family Symbolic Dynamics Topological Conjugacy Chaos Structural Stability Sarlovskiis Theorem The Schwarzian Derivative Bifurcation Theory Another View of Period Three Maps of the Circle Morse-Smale Diffeomorphisms Homoclinic Points and Bifurcations The Period-Doubling Route to Chaos The Kneeding Theory… 

Chapter 2 Preliminaries of Nonlinear Dynamics and Chaos

  • Physics
  • 2019
This chapter provides a brief review of some concepts and tools related to the subject of the monograph – chaos suppression, chaos synchronization, and chaotification. After a quick review of the

Resonances in skew and reducible quasi-periodic Hopf bifurcations

Two types of quasi-periodic Hopf bifurcations are known, in which a Whitney smooth family of quasi-periodic attractors loses its hyperbolicity. One is the reducible case, where the normal linear

Chaos and quasi-periodicity in diffeomorphisms of the solid torus

This paper focuses on the parametric abundance and the 'Cantorial' persistence under perturbations of a recently discovered class of strange attractors for diffeomorphisms, the so-called


In this article, we studied that no homeomorphism on unit interval into itself is chaotic in the sense of R.L. Devaney. We also studied the behavior of orbits of points in the dynamical system

Asymptotic periodicity and banded chaos

Dynamical Systems and Hyperbolicity

In this chapter, a definition of the dynamical system is discussed and some important classes like continuous-time and discrete-time systems, conservative and dissipativc systems, autonomous and non-autonomous systems are introduced.

Robust and Nonrobust Dynamical Systems: Classification of Attractor Types

We consider a class of autonomous continuous-time dynamical systems with phase space dimension N ≥ 3. Besides robust systems similar to Andronov–Pontryagin systems on the plane, there appears a class

Periodicity versus Chaos in One-Dimensional Dynamics

It is shown that maps with strong chaotic properties appear with positive frequency in parameter space in the population models of the Ricker and the Hassell families.

One-dimensional chaos in a system with dry friction: analytical approach

We introduce a new analytical method, which allows to find chaotic regimes in non-smooth dynamical systems. A simple mechanical system consisting of a mass and a dry friction element is considered.