Monotone dynamical systems : an introduction to the theory of competitive and cooperative systems / Hal L. Smith.

Smith, Hal L., author.
Providence, Rhode Island : American Mathematical Society, [1995]
Mathematical surveys and monographs ; no. 41.
Mathematical surveys and monographs, 0076-5376 ; volume 41
1 online resource (186 p.)
Differentiable dynamical systems.
Monotonic functions.
Electronic books.
""Contents""; ""Preface""; ""Chapter 1. Monotone Dynamical Systems""; ""0. Introduction""; ""1. Definitions and Preliminary Results""; ""2. The Convergence Criterion""; ""3. The Limit Set Dichotomy""; ""4. Quasiconvergence is Generic""; ""5. Remarks and Discussion""; ""Chapter 2. Stability and Convergence""; ""0. Introduction""; ""1. Stability""; ""2. The Order Interval Trichotomy""; ""3. Some Global Results""; ""4. Generic Convergence to Equilibrium""; ""5. Unstable Equilibria and Connecting Orbits""; ""6. Remarks and Discussion""
""Chapter 3. Competitive and Cooperative Differential Equations""""0. Introduction""; ""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""; ""7. Remarks and Discussion""; ""Chapter 4. Irreducible Cooperative Systems""; ""0. Introduction""; ""1. Strong Monotonicity""; ""2. A Biochemical Control Circuit""; ""3. Stability and the Perron-Frobenius Theorem""; ""4. Competition and Migration""; ""5. Smale's Construction""; ""6. Remarks and Discussion""
""Chapter 5. Cooperative Systems of Delay Differential Equations""""0. Introduction""; ""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""; ""8. Remarks and Discussion""; ""Chapter 6. Nonquasimonotone Delay Differential Equations""; ""0. Introduction""; ""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""; ""6. Remarks and Discussion""; ""Chapter 7. Quasimonotone Systems of Parabolic Equations""; ""0. Introduction""; ""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""""8. Remarks and Discussion""; ""Chapter 8. A Competition Model""; ""0. Introduction""; ""1. The Model""; ""2. A Single Population""; ""3. Stability of the Equilibria E[sub(0)], E[sub(1)], E[sub(2)]""; ""4. Coexistence""; ""5. Remarks and Discussion""; ""Appendix. Chain Recurrence""; ""Bibliography""; ""Index""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""H""; ""I""; ""K""; ""L""; ""M""; ""N""; ""N""; ""O""; ""P""; ""Q""; ""R""; ""S""; ""T""; ""U""; ""V""; ""W""
Description based upon print version of record.
Includes bibliographical references (pages 167-171) and index.
Description based on print version record.
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