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Stability of Linear and Nonlinear Compartmental Systems

Wiersma, Alida (2018) Stability of Linear and Nonlinear Compartmental Systems. Master's Thesis / Essay, Applied Mathematics.


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This thesis discusses properties that are related to the existence and stability of equilibria of linear and nonlinear compartmental systems. First, linear compartmental systems are considered and necessary and sufficient conditions for the system to be asymptotically stable will be given. Furthermore, for a class of nonlinear compartmental systems known as donor-controlled compartmental systems, sufficient conditions for boundedness of solutions and existence and uniqueness of an equilibrium are given. In addition a necessary condition for the existence of an equilibrium is given for compartmental systems with capacity constraints using the maximum flow of a network. Finally we show that the theory for compartmental systems can be applied to traffic networks and a necessary and sufficient condition for the existence of an equilibrium for traffic networks with demand functions is given.

Item Type: Thesis (Master's Thesis / Essay)
Supervisor name: Besselink, B.
Degree programme: Applied Mathematics
Thesis type: Master's Thesis / Essay
Language: English
Date Deposited: 12 Nov 2018
Last Modified: 13 Nov 2018 11:23

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