Cooperation is the second kind of interaction that can occur between two species. As in the case of competition, the interaction creates an unstable +feedback loop because two positive links (see figure). The extended logistic equation for a species receiving benefits from a cooperator is
This equation specifies the rate of change of each species as its maximum rate of change (Ai), minus the effect of intraspecific competition (Cii * Ni), plus the effect of interspecific cooperation (Cij * Nj). The zero growth isocline for species i is, therefore,
This isocline is a straight line with an intercept at Ki on the Ni-axis and increasing thereafter with Nj (see figure). NOTE the two-species trajectory, the gray line starting at the magenta spot and converging to the equilibrium point.
This model has a stable community equilibrium when the combined effect of intraspecific competition is stronger than the combined effect of interspecific competition
Of course we can include non-linear intraspecific by including the coefficient of curvature Q in the model.