摘要：An analytical and computational framework for the derivation of solitary solutions to biological systems describing the cooperation and
competition of species and expressed by the system of Riccati equations coupled with multiplicative terms is presented in this paper. It
is demonstrated that relationships between these solitary solutions
can be either direct or inverse. Thus, an infinitesimal perturbation of
one population would lead to an infinitesimal change in the other
population – if only both solitary solutions are coupled with the
direct relationship. But, in general, that is not true if solitary solutions
are coupled with the inverse relationship – an infinitesimal perturbation of one population may result into a non-infinitesimal change
in the other population. Necessary and sufficient conditions for the
existence of solitary solutions are derived in the space of the system’s
parameters and initial conditions.
关键词：Solitary solution ; Riccati equation ; multiplicative coupling ; existence
