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Dynamical Systems in Population Biology pp 1–41Cite as

Dissipative Dynamical Systems

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Abstract

There are many discrete-time population models governed by difference equations (or maps), and as we mentioned in the Preface, the dynamics of a periodic differential system can be investigated via its associated Poincaré map. The aim of this chapter is to introduce basic definitions and develop main tools in the theory of discrete dynamical systems. In Section 1.1 we present concepts of limit sets and attractors and some fundamental theorems such as the LaSalle invariance principle, the asymptotic fixed point theorem, and the global attractor theorems.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL, Canada

    Xiao-Qiang Zhao

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Zhao, XQ. (2017). Dissipative Dynamical Systems. In: Dynamical Systems in Population Biology. CMS Books in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-56433-3_1

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