The existence of globally stable equilibria of n-dimensional lotka-volterra systems

Abstract

Criteria for the existence of globally stable equilibria in Lotka-Volterra systems are provided by applying matrix analysis to seek for Volterra multiplier. The opposite of the considered community matrix A belongs to such a class of matrix class S, that whose associated graph being a tree generated by trees of competition model, of cooperative model and of preypredator model and that the matrix A satisfies the criteria given.

Keywords:

• Lotka-Volterra system
• equilibrium
• global stability
• Volterra multiplier

Research supported by the National 863 Project and the NSF of China

Research supported by the National 863 Project and the NSF of China

Notes

Research supported by the National 863 Project and the NSF of China