Global asymptotic behavior of the n-species lotka-volterra tree systems with continuous time delay^*

^*Research supported by the National 863 Project and the NST .of China

Abstract

In n-species Lotka-vol terra, tree systems with continuous time delay the criteria are obtained for the existence of a nontrival and nonnegative globally asymptotical stable equilibrium by applying quadratic form theory and introducing the degree of the matrix map. The sufficient condition is uniform to competition, symbiotic and prey-predator models. Furthermore, we also give sufficient conditions of positive stable equilibria in symhiotic tree systems.

Keywords:

• Lotlka-Volterra system
• equilibrium
• global stability
• time delay

^*Research supported by the National 863 Project and the NST .of China

^*Research supported by the National 863 Project and the NST .of China

Notes

^*Research supported by the National 863 Project and the NST .of China