Three-species Interaction

Abstract

The expression of the third-order term of Eq. (3.9), i.e. Eq. (9.1), finds an interesting application. This term can be negative and therefore contribute to stabilizing the system only if

$$ {{\text{S}}_{{\text{k 0}}}}{{\text{S}}_{0{\text{L}}}}{S_{LK{\text{ }}}} > {\text{ 0}} $$

(10.1)

since for a sufficiently small interaction

$$ {S_{pq}}{\text{ (}}{H_{qp}}{\text{ - }}{S_{qp}}{H_{00}}) < 0 $$

in the argument using real functions. This stability condition (10.1), applied to a system composed of three species interacting with one another, serves frequently as the selection rule of chemical interactions.