Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems
About this Title
Hal L. Smith, Arizona State University, Tempe
Publication: Mathematical Surveys and Monographs
Publication Year 1995: Volume 41
ISBNs: 978-0-8218-4487-8 (print); 978-1-4704-1272-2 (online)
MathSciNet review: MR1319817
MSC: Primary 34-02; Secondary 34C35, 34Cxx, 34Dxx, 34Kxx, 35K57, 54H20, 58Fxx
This book presents comprehensive treatment of a rapidly developing area with many potential applications: the theory of monotone dynamical systems and the theory of competitive and cooperative differential equations. The primary aim is to provide potential users of the theory with techniques, results, and ideas useful in applications, while at the same time providing rigorous proofs. Among the topics discussed in the book are continuous-time monotone dynamical systems, and quasimonotone and nonquasimonotone delay differential equations. The book closes with a discussion of applications to quasimonotone systems of reaction-diffusion type. Throughout the book, applications of the theory to many mathematical models arising in biology are discussed.
Requiring a background in dynamical systems at the level of a first graduate course, this book is useful to graduate students and researchers working in the theory of dynamical systems and its applications.
Students and researchers in dynamical systems theory, applied mathematicians, and scientists.
Table of Contents
- 1. Monotone dynamical systems
- 2. Stability and convergence
- 3. Competitive and cooperative differential equations
- 4. Irreducible cooperative systems
- 5. Cooperative systems of delay differential equations
- 6. Nonquasimonotone delay differential equations
- 7. Quasimonotone systems of parabolic equations
- 8. A competition model