Global stability of n—dimensional

Abstract

In this paper, we deal with the global asymptotic stability of n—dimensional Loth-Volterra system with time dependent coefficients. By constructing suitable Lyapunov functions, we generalizeTheorems 3.1 and 3.2 of 161 to our n-dimensional case and therefore have solved the open problem given in 161. We also discuss the global stability of the periodic solution of the system when all the coefficients of the system are periodic. For the case of n = 2, we have improved the corresponding results in 161.

Keywords:

• Lyapunov functions
• global stability
• periodic solution