Description

This course is about the basic theory of infinite dimensional dynamical systems. The contents include the dynamical systems approach to evolution equations; dissipative dynamical systems(limit sets and global attractors, chain transitive sets, uniform persistence); monotone dynamics (attracting order intervals and connecting orbits, global attractivity and convergence, and
subhomogeneous maps); traveling waves and spreading speeds; and applications to population biology.

Prerequisites

Ordinary and partial differential equations, dynamical systems, functional analysis, and point set topology at the undergraduate level.

Textbook

• X. Zhao, Dynamical Systems in Population Biology, second edition, Springer-Verlag, New York, 2017.

References

• J. K. Hale, Asymptotic Behavior of Dissipative Systems,
  Amer. Math. Soc., Providence, 1988.
• H. L. Smith, Monotone Dynamical Systems, An Introduction to the
  Theory of Competitive and Cooperative Systems, Mathematical Surveys and Monographs 41, Amer. Math. Soc., Providence, RI,1995.