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 recall 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 theorem.
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© 2003 Springer Science+Business Media New York
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Zhao, XQ. (2003). Dissipative Dynamical Systems. In: Dynamical Systems in Population Biology. Canadian Mathematical Society / Société mathématique du Canada. Springer, New York, NY. https://doi.org/10.1007/978-0-387-21761-1_1
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DOI: https://doi.org/10.1007/978-0-387-21761-1_1
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-1815-4
Online ISBN: 978-0-387-21761-1
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