A criterion of global convergence to equilibrium for differential systems. Application to Lotka-Volterra systems
Résumé
We study a rather general class of systems of ordinary differential equations in n-space that can be expressed as the difference of a quasi-monotone and a monotone increasing system. We associate to the system another cooperative system in 2n-space. We obtain a sufficent condition of convergence to equilibrium, and apply it to linear and Lotka-Volterra systems.