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 |
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| 100 | 1 | |a Smith, Hal L. |0 http://id.loc.gov/authorities/names/n94042965 |1 http://viaf.org/viaf/19830653 | |
| 245 | 1 | 0 | |a Monotone dynamical systems : |b an introduction to the theory of competitive and cooperative systems / |c Hal. L. Smith. |
| 260 | |a Providence, R.I. : |b American Mathematical Society, |c c1995. | ||
| 300 | |a x, 174 p. : |b ill. ; |c 27 cm. | ||
| 336 | |a text |b txt |2 rdacontent |0 http://id.loc.gov/vocabulary/contentTypes/txt | ||
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| 490 | 1 | |a Mathematical surveys and monographs ; |v v. 41 | |
| 504 | |a Includes bibliographical references (p. 167-171) and index. | ||
| 505 | 0 | 0 | |g Ch. 1. |t Monotone Dynamical Systems. |g 2. |t The Convergence Criterion. |g 3. |t The Limit Set Dichotomy. |g 4. |t Quasiconvergence is Generic -- |g Ch. 2. |t Stability and Convergence. |g 1. |t Stability. |g 2. |t The Order Interval Trichotomy. |g 3. |t Some Global Results. |g 4. |t Generic Convergence to Equilibrium. |g 5. |t Unstable Equilibria and Connecting Orbits -- |g Ch. 3. |t Competitive and Cooperative Differential Equations. |g 1. |t The Kamke Condition. |g 2. |t Positively Invariant Sets and Monotone Solutions. |g 3. |t Main Results. |g 4. |t Three Dimensional Systems. |g 5. |t Alternative Cones. |g 6. |t The Field-Noyes Model -- |g Ch. 4. |t Irreducible Cooperative Systems. |g 1. |t Strong Monotonicity. |g 2. |t A Biochemical Control Circuit. |g 3. |t Stability and the Perron-Frobenius Theorem. |g 4. |t Competition and Migration. |g 5. |t Smale's Construction -- |g Ch. 5. |t Cooperative Systems of Delay Differential Equations. |g 1. |t The Quasimonotone condition. |g 2. |t Positively Invariant Sets, Monotone Solutions, and Contracting Rectangles. |g 3. |t Eventual Strong Monotonicity. |g 4. |t Generic Convergence for Cooperative and Irreducible Systems. |g 5. |t Stability of Equilibria. |g 6. |t A Biochemical Control Circuit with Delays. |g 7. |t Competition with Time Delays -- |g Ch. 6. |t Nonquasimonotone Delay Differential Equations. |g 1. |t The Exponential Ordering. |g 2. |t The Strong Order Preserving Property. |g 3. |t Generic Convergence to Equilibrium. |g 4. |t Stability of Equilibria. |g 5. |t A Model of an Adult Fly Population -- |g Ch. 7. |t Quasimonotone Systems of Parabolic Equations. |g 1. |t Parabolic Systems: The Basic Setup. |g 2. |t Maximum Principles. |g 3. |t Positively Invariant Sets, Comparison and Monotonicity. |g 4. |t The Strong Order Preserving Property. |g 5. |t Generic Convergence for Cooperative and Irreducible Systems. |g 6. |t Stability of Equilibria. |g 7. |t The Biochemical Control Circuit with Diffusion -- |g Ch. 8. |t A Competition Model. |g 1. |t The Model. |g 2. |t A Single Population. |g 3. |t Stability of the Equilibria E[subscript 0], E[subscript 1], E[subscript 2]. |g 4. |t Coexistence. |t Appendix. Chain Recurrence. |
| 650 | 0 | |a Differentiable dynamical systems. |0 http://id.loc.gov/authorities/subjects/sh85037882 | |
| 650 | 0 | |a Monotonic functions. |0 http://id.loc.gov/authorities/subjects/sh85086979 | |
| 650 | 7 | |a Differentiable dynamical systems. |2 fast |0 http://id.worldcat.org/fast/fst00893426 | |
| 650 | 7 | |a Monotonic functions. |2 fast |0 http://id.worldcat.org/fast/fst01025723 | |
| 830 | 0 | |a Mathematical surveys and monographs ; |v no. 41. | |
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| 928 | |t Library of Congress classification |a QA614.8.S630 1995 |l Eck |c Eck-Eck |i 2297296 | ||
| 927 | |t Library of Congress classification |a QA614.8.S630 1995 |l Eck |c Eck-Eck |b 42490037 |i 3259048 | ||