Abstract
Using linear stability analysis, the qualitative stability properties of open nonlinear chemical systems, in which reactions of any order may occur, will be studied. Systems will be classified in three fundamental classes: trees, cycles and loops, according to their knot graphs. The study of the Jacobian matrix for the kinetic equations of the system shows that the symmetrizability by a particular procedure (calledD-symmetrizability) is a sufficient condition for stability. It has been proved that tree-graphs always satisfy the above condition. For the cycle-graphs, theD-symmetrizability condition leads to a cyclic relation between forward and reverse steady state flows. The stability may be assured, even if the cyclic relation is not satisfied, providing that the “symmetry breaking” be lower than an upper bound; further alternative criteria for stability of cycles have been derived. All these results are independent of the number of diffusive exchanges with the environment.
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Beretta, E., Vetrano, F., Solimano, F. et al. Some results about nonlinear chemical systems represented by trees and cycles. Bltn Mathcal Biology 41, 641–664 (1979). https://doi.org/10.1007/BF02462420
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DOI: https://doi.org/10.1007/BF02462420