Lyapunov functionals for two-species mutualisms

We analyze the dynamics of a general model of two-species mutualistic interaction given in an abstract, unspecified form, which fits several commonly used concrete models. Sufficient conditions for the global stability of the positive equilibrium are obtained by means of employing Lyapunov’s second method, for functionals which are defined ad hoc and are strictly more general than both quadratic and Volterra functionals. It is observed that the complexity of such conditions increases drastically when key monotonicity properties are weakened.