【作者】 刘雁； 张家忠； 孙旭；

【Author】 Liu Yan1,2,Zhang Jiazhong3,Sun Xu3 1.School of Mechatronics,Northwestern Polytechnical University,Xi’an 710072 2.School of Automation,Northwestern Polytechnical University,Xi’an 710072 3.School of Energy and Power Engineering,Xi’an Jiaotong University,Xi’an 710049

【机构】 西北工业大学机电学院； 西北工业大学自动化学院； 西安交通大学能源与动力工程学院；

【摘要】 基于非线性动力学理论,研究了小世界网络模型的非线性动力学现象。首先,在已有的小世界网络非线性动力学模型基础上,即时滞微分发展方程,对其中随参数变化系统的平衡状态失稳而出现的Hopf分岔进行了数值分析;然后,根据Hopf分岔的分析结果,对系统在一定参数条件下周期振荡的产生和消失进行了解释。研究表明:该系统蕴含有丰富的非线性动力学行为,通过建立合理的控制方程,可以对该类"非均匀"动力系统进行深入地理论分析,探索出产生各类复杂非线性动力学现象的机理,从而实现对该类网络系统的有效控制。更多还原

【Abstract】 From viewpoint of nonlinear dynamics,the nonlinear dynamic phenomena of the small-world networks are studied in some details.The small-world networks model,a set of evolution equations with time delay,is used to approach the nonlinear dynamics of networks,and the stability and Hopf bifurcation of the equilibrium state are investigated numerically,as the bifurcation parameter is varied.Furthermore,the intermittency phenomena in the networks are explained based on the analysis of Hopf bifurcation,and the results can gain a fundamental understanding for the instability in the networks.As the conclusion,it is shown that there exist a rich variety of nonlinear dynamic phenomena in the system governed by the small-works networks model,and the system can be controlled properly as the model is improved and the nature of the complex phenomena is gained.更多还原