对具有时延的小世界网络模型进行了分析,研究了网络模型平衡点的局部稳定性,把时延看作分岔参数,推导出了霍普分叉产生的参数条件.当系统存在霍普分叉时,系统会产生振荡、失稳等现象,为了稳定该网络模型,提出了一种脉冲控制霍普分叉的方法.分析了脉冲控制系统全局渐近稳定的充分条件,通过数值仿真验证了此控制方法的有效性.
A delayed small-world network model was analyzed. The local stability of the equilibrium in the network model was investigated. Taking the time delay as a bifurcation parameter, the parameter condition where Hopf bifurcation occurred was deduced. This Hopf bifurcation phenomenon appears, which will cause the system to produce continues vibration and instability phenomenon. In order to stabilize the network model, an impulsive control bifurcation method was proposed. Analyzed the sufficient conditions under which an impulsive system is asymptotically stable. Numerical simulation verified the validity of this control method.