中文摘要：

针对一类具有3个离散时滞的合作系统,以3个时滞τ_1,τ_2,τ的两种组合为分支参数,基于对特征方程根的分析和规范型理论,考察两种不同情形下平衡点的稳定性及局部Hopf分支产生的充分条件,得到了确定分支周期解稳定性及分支方向的算法和计算公式,给出了全局Hopf分支存在性的理论证明,并通过数值模拟验证了分支周期解的存在性可由局部延拓至全局.

英文摘要：

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.