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.
ASJC Scopus subject areas
- Applied Mathematics