Course Control and System Theory of Rational Systems Motivated by
the Life Sciences
Homeworkset 6
Date issued: 11 October 2018.
Date due: 18 October 2018.
1. Investigate the stability of a polynomial cyclic positive reaction system of state-space dimension
nx = 3 of which the reaction network is irreducible and of which the system is also
irreducible. Questions to be discussed include: (1) Does there exist a unique steady state
within each stoichoimetric compatability subset? (2) If there exists a unique steady state with
a stoichiometric compatability subset, is that state globally asymptotically stable for initial
states in that subset possibly intersected with the interior of the positive orthant?
2. Investigate the stability of a polynomial mammillary positive reaction system of state-space
dimension nx = 3 of which the reaction network is irreducible and of which the system is
also irreducible.
Contact the lecturer J.H. van Schuppen if you have problems with these problems. Possibly additional
assumptions have to be imposed to make the problem solvable.
Reading advice for Lecture 6
Please read of the lecture notes the Sections 6.5, 6.6, 6.7, and 6.8.
Reading advice for the future Lecture 7
On Thursday 18 October, Lecture 7 will be presented. Please read of the lecture notes the Sections
7.1 - 7.6. As mentioned before, this is a recommendation only.
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