惯性时滞神经网络共振余维二分岔  

Resonate Codimension Two Bifurcation in an Inertial Two-neuron System with Time Delay

作　　者：刘群[1] 祝红芳[2] 

机构地区：[1]重庆邮电大学计算机学院,重庆400065 [2]江西工业职业技术学院,江西南昌330039

出　　处：《南昌大学学报（理科版）》2009年第5期476-480,共5页Journal of Nanchang University(Natural Science)

基　　金：国家973前期基础研究项目(2008CB317111);国家自然科学基金项目(60573047);重庆市自然科学基金(CSTC2007BB2386);重庆市教委基础研究项目(KJ090803);重庆邮电大学博士启动基金资助项目(A2009-10)

摘　　要：研究惯性时滞神经网络系统的共振余维二分岔,讨论了时滞的变化对系统余维二分岔的影响。利用Hopf分岔定理获得了系统余维二分岔存在的充要条件,借助中心流形定理和正规型理论约化了系统,从理论上分析了共振余维二分岔在平衡点附近的动力学行为,以及由此引发的分岔周期解的方向以及稳定性条件,最后通过实验仿真验证了理论分析的正确性。It studied the resonate codimension two bifurcation in an inertial two - neuron system with time delay, and discussed the influence to the system by the time delay. A sufficient and necessary condition for the existence of codimension two bifurcation is obtained via Hopf bifurcation theorem. With aid of center manifold theorem and the normal form theory, the system is reduced to the center manifold, then the dynamic behavior in the vicinity of the resonate double Hopf bifurcation, including the direction of Hopf bifurcation and stability of bifurcating periodic solution, is investigated. The analytical results are found to be in good agreement with results obtained by the numerical simulations.

关 键 词：时滞 共振 惯性项 余维二分岔 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]