Semidynamical Systems and Delay Equations
An autonomous system of delay differential equations is shown to generate a semidynamical system on the space C of continuous functions on the delay interval. Omega limit sets are defined and shown to have the same properties as for ODEs, with minor exceptions, although they are subsets of C. The dynamics of the delayed logistic equation and the chemostat model are treated in detail. A special class of delay equations is shown to generate monotone dynamics; solutions converge to equilibrium. Liapunov functions and the LaSalle invariance principle areused to study the dynamics of a delayed logistic equation with both instantaneous and delayed density dependence
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