Monotone dynamical systems : an introduction to the theory of competitive and cooperative systems /
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| Author / Creator: | Smith, Hal L. |
|---|---|
| Imprint: | Providence, R.I. : American Mathematical Society, c1995. |
| Description: | x, 174 p. : ill. ; 27 cm. |
| Language: | English |
| Series: | Mathematical surveys and monographs ; v. 41 Mathematical surveys and monographs ; no. 41. |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/1739274 |
Table of Contents:
- Ch. 1. Monotone Dynamical Systems. 2. The Convergence Criterion. 3. The Limit Set Dichotomy. 4. Quasiconvergence is Generic
- Ch. 2. Stability and Convergence. 1. Stability. 2. The Order Interval Trichotomy. 3. Some Global Results. 4. Generic Convergence to Equilibrium. 5. Unstable Equilibria and Connecting Orbits
- Ch. 3. Competitive and Cooperative Differential Equations. 1. The Kamke Condition. 2. Positively Invariant Sets and Monotone Solutions. 3. Main Results. 4. Three Dimensional Systems. 5. Alternative Cones. 6. The Field-Noyes Model
- Ch. 4. Irreducible Cooperative Systems. 1. Strong Monotonicity. 2. A Biochemical Control Circuit. 3. Stability and the Perron-Frobenius Theorem. 4. Competition and Migration. 5. Smale's Construction
- Ch. 5. Cooperative Systems of Delay Differential Equations. 1. The Quasimonotone condition. 2. Positively Invariant Sets, Monotone Solutions, and Contracting Rectangles. 3. Eventual Strong Monotonicity. 4. Generic Convergence for Cooperative and Irreducible Systems. 5. Stability of Equilibria. 6. A Biochemical Control Circuit with Delays. 7. Competition with Time Delays
- Ch. 6. Nonquasimonotone Delay Differential Equations. 1. The Exponential Ordering. 2. The Strong Order Preserving Property. 3. Generic Convergence to Equilibrium. 4. Stability of Equilibria. 5. A Model of an Adult Fly Population
- Ch. 7. Quasimonotone Systems of Parabolic Equations. 1. Parabolic Systems: The Basic Setup. 2. Maximum Principles. 3. Positively Invariant Sets, Comparison and Monotonicity. 4. The Strong Order Preserving Property. 5. Generic Convergence for Cooperative and Irreducible Systems. 6. Stability of Equilibria. 7. The Biochemical Control Circuit with Diffusion
- Ch. 8. A Competition Model. 1. The Model. 2. A Single Population. 3. Stability of the Equilibria E[subscript 0], E[subscript 1], E[subscript 2]. 4. Coexistence. Appendix. Chain Recurrence.