Coexistence for species sharing a predator.
A class of equations describing the dynamics of two preys sharing a common predator is considered. Even though the boundary and internal dynamics can exhibit oscillatory behavior, it is shown that these equations are permanent if and only if they admit a positive equilibrium. Going beyond permanence, a subclass of equations are constructed that are almost surely permanent but not permanent; there exists an attractor in the positive orthant that attracts Lebesgue almost every (but not every) initial condition.
scientific article; zbMATH DE number 2033007