Equivalence between S-systems and Volterra systems (Q1072466)

The authors discuss the wide range of applicability of so-called S- systems of differential equations \[ \dot x_ i=\alpha_ i\prod^{n}_{j=1}x_ j^{g_{ij}}-\beta_ i\prod^{n}_{j=1}x_ j^{h_{ij}},\quad \alpha_ i\geq 0,\quad \beta_ i\geq 0, \] in describing biological and physical phenomena. Volterra systems \(\dot N_ i=N_ i(a_ i-\sum^{m}_{j=1}p_{ij}N_ j)\) have also found widespread use, particularly in population dynamics. In this paper it is shown that S-systems and Volterra systems are equivalent, i.e. any Volterra system can be transformed into an S-system and conversely. The implications of this equivalence in modelling applications are discussed.