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Monotone dynamical systems. (English) Zbl 1094.34003
Cañada, A.(ed.) et al., Ordinary differential equations. Vol. II. Amsterdam: Elsevier/North Holland (ISBN 0-444-52027-9/hbk). Handbook of Differential Equations, 239-357 (2005).
The paper, a part of the handbook of differential equations, is a substantial survey on dynamical systems in ordered spaces. The main focus is on the asymptotical behaviour of monotone dynamical systems. The paper contains seven chapters organized as follows: 0. Introduction; 1. Strongly order-preserving semiflows; 2. Generic convergence and stability; 3. Ordinary differential equations; 4. Delay differential equations; 5. Monotone maps; 6. Semilinear parabolic equations. At the end of the paper, 248 references are listed, covering a big part of the existing literature on the subject. For the entire collection see [Zbl 1074.34003].

34-02Research monographs (ordinary differential equations)
34C12Monotone systems
34D05Asymptotic stability of ODE
34D09Dichotomy, trichotomy
34K12Growth, boundedness, comparison of solutions of functional-differential equations
35K55Nonlinear parabolic equations
47H07Monotone and positive operators on ordered topological linear spaces