Abstract
In the last chapter, we saw that compartimentai matrices had eigenvalues whose real part, if not zero, was negative. Hence, any solution to the associated differential equation was asymptotically stable. We also saw that positive initial values lead to non-negative solutions. However, there is still the possibility that a solution have a zero component in finite time. We also would like to determine structural conditions under which the asymptotic levels are nonzero; i.e. conditions for which x(t) > 0 as t → ∞. We also consider a method for simplifying the structure. Certain cases with a particular structure are shown to have associated dynamical behavior.
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© 1999 Springer Science+Business Media New York
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Walter, G.G., Contreras, M. (1999). Structure and Dynamical Properties. In: Compartmental Modeling with Networks. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1590-5_20
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DOI: https://doi.org/10.1007/978-1-4612-1590-5_20
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7207-6
Online ISBN: 978-1-4612-1590-5
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