中文摘要：

研究一类具有时滞的游荡蜘蛛模型,选择时滞τ为分支参数,当时滞τ通过一系列的临界值时,Hopf分支产生,即当时滞τ通过某些临界值时,从平衡点处产生一簇周期解。运用中心流型定理和规范型理论,研究分支周期解的特性,包括Hopf分支的稳定性、分支方向、周期。数值模拟验证了结论的正确性,补充了已有的结果。

英文摘要：

A delayed wandered spider model is investigated. By choosing the delay r as a bifurcation parameter, it is shown that Hopf bifurcation can occur when τ passes a sequence of critical values. This means that a family of periodic solutions bifurcates from the equilibrium when the bifurcation parameter exceeds a critical value. Applying the center manifold theory and normal form theorem, the nature of bifurcation periodic solutions （for example, the stability, the solution ets. ） is investigated. Some numerical simulations direction and the periodic of Hopf bifurcation are given to justify the theoretical analysis resuits. The results complement previously known results.