Abstract:

This paper presents an analysis of the periodic solutions of a higher dimensional network with time delay. First, using the characterisic root methods, we investigated the linear stability analysis and local existence of periodic solutions bifurcated from the trivial equilibrium. Especially, an efficient numerical method is presented to find a periodic solution and numerically determine its stability by the computation of the dominant Floquet multipliers. This paper gives a new mehod to determine the stability of delayed differential equaitons.

Key words:  ring network, periodic solutions, Hopf bifurcation, Floquet multipliers