Strong Monotonicity, A Biochemical Control Circuit, Stability and the Perron-Frobenius Theorem
| Week | Course Content | Course Video |
|---|---|---|
| Review on General Dynamical System | Watch Online | |
| Monotone Dynamical System Definitions Monotone Strongly monotone Strongly order preserving (SOP) | Watch Online | |
| Hirsch’s Convergence Theorem No attracting periodic orbit in monotone system | Watch Online | |
| Non-ordering of limit sets Limit set dichotomy Generic quasi-convergence | Watch Online | |
| Competitive and Cooperative Differential Equations Kamke Condition | Watch Online | |
| Positively invariant sets and Monotone Solutions Non-oscillation principle | Watch Online | |
| Topological Equivalence of flow of competitive or cooperative n-d systems to a flow on (n-1)-d system of Lipschitz differential equations | Watch Online | |
| Poincare-Bendixson Theorem of 3-d competitive systems Alternative Cones The Field-Noyes Model | Watch Online | |
| Strong Monotonicity A Biochemical Control Circuit Stability and the Perron-Frobenius Theorem | Watch Online | |
| Irreducible Cooperative Systems Competition and Migration Smale’s Construction | Watch Online | |
| Quasimonotone Systems of Parabilic Equations The Basic Setup, Maximum Principles Positively Invariant Sets Comparison and Monotonicity The Strong Order Preserving Property | Watch Online | |
| Irreducible Cooperative Systems A Biochemical Control Circuit Two Patch Competitive Models | Watch Online | |
| Quasimonotone Systems of Parabilic Equations The Basic Setup Strong Parabilic Maximum Principles | Watch Online | |
| Comparison Principle Krein-Rutman Theorem Weak Maximum Principle Positively Invariant Sets Comparison and Monotonicity | Watch Online | |
| Krein-Rutman Theorem Reaction-Diffusion system Principle eigenvalue Two species competition in the flow reactor model | Watch Online |
COURSE
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