The underlying linear dynamics of some positive polynomial systems

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. -- Highlights: ► The underlying linear dynamics for a class of QP systems have been determined. ► The dynamically similar linear dynamics for kinetic systems have been determined. ► Structural similarities of QP and kinetic system classes have been established.