Abstract
As we illustrated in the Preface, some population models can generate continuous- or discrete-time dynamical systems with monotonicity: Ordered initial states lead to ordered subsequent states. This chapter is aimed at monotone dynamics. We are primarily interested in some global results that may be effectively applied to both discrete-time and periodic biological systems. In Section 2.1 we prove the existence and global attractivity of an order interval defined by two fixed points, and a theorem on fixed points and connecting orbits for continuous and monotone maps on an ordered Banach space E.
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© 2003 Springer Science+Business Media New York
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Zhao, XQ. (2003). Monotone Dynamics. 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_2
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DOI: https://doi.org/10.1007/978-0-387-21761-1_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-1815-4
Online ISBN: 978-0-387-21761-1
eBook Packages: Springer Book Archive