Finite Dimensional State Representation of Linear and Nonlinear Delay Systems

Diekmann, O., Gyllenberg, M., & Metz, J.A.J. (2018). Finite Dimensional State Representation of Linear and Nonlinear Delay Systems. Journal of Dynamics and Differential Equations 30 (4) 1439-1467. 10.1007/s10884-017-9611-5.

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We consider the question of when delay systems, which are intrinsically infinite dimensional, can be represented by finite dimensional systems. Specifically, we give conditions for when all the information about the solutions of the delay system can be obtained from the solutions of a finite system of ordinary differential equations. For linear autonomous systems and linear systems with time-dependent input we give necessary and sufficient conditions and in the nonlinear case we give sufficient conditions. Most of our results for linear renewal and delay differential equations are known in different guises. The novelty lies in the approach which is tailored for applications to models of physiologically structured populations. Our results on linear systems with input and nonlinear systems are new.

Item Type: Article
Uncontrolled Keywords: Linear chain trick; Delay-differential equation; Renewal equation; Markov chain; Physiologically structured populations; Epidemic models
Research Programs: Evolution and Ecology (EEP)
Depositing User: Romeo Molina
Date Deposited: 06 Sep 2017 07:55
Last Modified: 27 Aug 2021 17:29

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