A perturbation-incremental scheme for studying Hopf bifurcation in delayed differential systems  

作　　者：CHUNG Kwok Wai 

机构地区：[1]Department of Mathematics, City University of Hong Kong Kowloon

出　　处：《Science China(Technological Sciences)》2009年第3期698-708,共11页中国科学（技术科学英文版）

基　　金：Supported by National Natural Science Funds for Distinguished Young Scholar (Grant No. 10625211);Key Program of National Natural Science Foundation of China (Grant No. 10532050);Program of Shanghai Subject Chief Scientist (Grant No. 08XD14044);Hong Kong Research Grants Council under CERG (Grant No. CityU 1007/05E)

摘　　要：A new method, called perturbation-incremental scheme (PIS), is presented to investigate the periodic solution derived from Hopf bifurcation due to time delay in a system of first-order delayed differential equations. The method is summarized as three steps, namely linear analysis at critical value, perturba- tion and increment for continuation. The PIS can bypass and avoid the tedious calculation of the center manifold reduction (CMR) and normal form. Meanwhile, the PIS not only inherits the advantages of the method of multiple scales (MMS) but also overcomes the disadvantages of the incremental harmonic balance (IHB) method. Three delayed systems are used as illustrative examples to demonstrate the validity of the present method. The periodic solution derived from the delay-induced Hopf bifurcation is obtained in a closed form by the PIS procedure. The validity of the results is shown by their consis- tency with the numerical simulation. Furthermore, an approximate solution can be calculated in any required accuracy.A new method, called perturbation-incremental scheme (PIS), is presented to investigate the periodic solution derived from Hopf bifurcation due to time delay in a system of first-order delayed differential equations. The method is summarized as three steps, namely linear analysis at critical value, perturbation and increment for continuation. The PIS can bypass and avoid the tedious calculation of the center manifold reduction (CMR) and normal form. Meanwhile, the PIS not only inherits the advantages of the method of multiple scales (MMS) but also overcomes the disadvantages of the incremental harmonic balance (IHB) method. Three delayed systems are used as illustrative examples to demonstrate the validity of the present method. The periodic solution derived from the delay-induced Hopf bifurcation is obtained in a closed form by the PIS procedure. The validity of the results is shown by their consistency with the numerical simulation. Furthermore, an approximate solution can be calculated in any required accuracy.

关 键 词：DELAYED differential equation perturbation-incremental scheme HOPF BIFURCATION synchronization center MANIFOLD 

分 类 号：O175[理学—数学]