Abstract:

For a class of cooperative systems with three discrete time delays, with two combinations of three time delays τ₁,τ₂,τ as bifurcation parameters, based on the analysis of the root of the characteristic equation and the standard theory, we investigated the stability of equilibrium points and the sufficient conditions of local Hopf bifurcation in two cases, and obtained the algorithms and calculation formulas for determining the stability and bifurcation direction of the bifurcation periodic solutions. We gave the theoretical proof of the existence of global Hopf bifurcation, and the existence of bifurcation periodic solutions from local to global can be verified by numerical simulations.

Key words: cooperative system, time delay, stability, local Hopf bifurcation, global Hopf bifurcation