Abstract
The conditions of structural dynamical similarity of two special classes of positive polynomial nonlinear systems, the class of quasi-polynomial systems (Brenig (1988) [1]) and that of reaction kinetic networks with mass action kinetics (Horn and Jackson (1972) [2]) are investigated in this Letter. It is shown that both system classes have an underlying reduced linear dynamics. By applying the theory of X-factorable systems (Samardzija et al. (1989) [9]), it can be shown that the reduced linear dynamics is qualitatively similar to the original one within the positive orthant when the original nonlinear system has a unique positive equilibrium point.
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