Convergence of solutions of nonlinear systems with integrable forcing term and its applications to a biological model

A non-autonomous nonlinear system with a time-variational forcing term is considered. For such a system, the global attraction of the origin is discussed, whose result is suggestive to an ecological problem as well because the system is reduced to a Lotka–Volterra predator–prey model with prey receiving an environmental time-variation by an appropriate transformation. A numerical simulation is also shown to suggest a new mathematical insight beyond our intuition.