On the Asymptotic Behavior of a Class of Deterministic Models of Cooperating Species

Source abstract

In this paper the global behavior of solutions of a class of ordinary differential equations modeling n cooperating biological species is determined. The class of systems includes the classical Lotka–Volterra systems as well as more realistic and more highly nonlinear systems. The fundamental tools are the Kamke theorem, results of M. W. Hirsch for so-called cooperative systems and the Perron–Frobenius theory of nonnegative matrices and its extensions.