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Biochemical reaction systems – system theory and decomposition

Nemcová J., van Schuppen J. H.

Control and Cybernetics

2013

Vol. 42, no. 1

183--215

Biochemical reaction networks may be modeled as biochemical reaction systems consisting of differential equations with rational functions. Biochemical reaction systems are defined as rational positive dynamic systems with inputs and outputs, and illustrated by examples. This formulation makes available the results from algebraic system theory for rational systems and a relation with computer algebra. It is shown how to decompose networks into subsystems and how to relate them to graphs. The realization problem for this class of systems is briefly discussed. Finally, control problems for biochemical reaction networks are formulated.

Patterns of boundedness of the rational system xn+1 = ...[wzór] and yn+1 = ...[wzór]

Camouzis E., Drymonis E., Ladas G.

Fasciculi Mathematici

2010

Nr 44

9-18

We establish the boundedness character of solutions of the rational system in the title, with the parameters α1, β1 positive and the remaining eight parameters nonnegative and with arbitrary nonnegative initial conditions such that the denominators are always positive. We present easily verifiable necessary and sufficient conditions, explicitly stated in terms of the parameters, which determine the boundedness character of the system.