## 留言板

 引用本文: 程福德. 一类扩张了的软弹簧型Duffing方程的紊动性态[J]. 应用数学和力学, 1991, 12(12): 1081-1085.
Cheng Fu-de. A Group of Chaotic Motion of Soft Spring Quadratic Duffing Equations[J]. Applied Mathematics and Mechanics, 1991, 12(12): 1081-1085.
 Citation: Cheng Fu-de. A Group of Chaotic Motion of Soft Spring Quadratic Duffing Equations[J]. Applied Mathematics and Mechanics, 1991, 12(12): 1081-1085.

## A Group of Chaotic Motion of Soft Spring Quadratic Duffing Equations

• 摘要: 本文用Melnikov函数方法讨论了一类扩张了的软弹簧型Duffing方程(k=1,2,3,…)在周期激励下的紊动现象.给出了出现二阶同宿切的条件.文中所采用的方法对于不能给出并宿轨道的显式的系统的研究是非常有用的.
•  [1] 李继彬,《浑沌与Melnikov方法》,重庆大学出版社(1989). [2] 李继彬、刘曾荣,一类二次系统周期扰动的浑沌性质,科学通报.30(7)(1985),491-495. [3] 李继彬、区月华.扰动双中心二次系统的全局分岔与浑沌性质.应用数学学报,11(3)(1988),312. [4] 李继彬、刘曾荣.几类非线性振动系统的浑沌性质.数学物理学报.11(2)(1985),195. [5] 刘曾荣、李继彬、林常.催化反应中的浑沌现象,应用数学和力学,7(1)(1986),43-49. [6] Greeie,Bernie and Philp J.Holmes,Repeated resonance and homoclinic bifurcation in a periodically forced family of oscillator,SIAM.Math Anal.,15,1(1984).69-77. [7] Holmes,Philp J.,Averaging and chaotic motion in forced oscillations,SIAM J.Appl.Aath.,38.1(1980). [8] Sander,Jan A.,Melnikov's method and averaging,The 1981 Oberwolfach Conference on Mathematics,D.Reided Publishing Co.,Dordrecht,Holland and Boston.U.S.A.(1982),171-181. [9] Kopel,Naney and B.Robert,Chaotic motion in the two-degree-of-freedom swing equations,IEEE Transaction on System,CAS-29,11(1982).738-746. [10] Guckenheimer,John and Philp J.Holmes.Nonlinear Oscillations,Dynamical Systems and Bifurcations of Vector Fields,New York,Berlin.Heidelberg.Tokyo(1984). [11] Salam,Fathi M.,The Melnikov technique for highly dissipative systems,SIAM J.Appl.Math.,47,2(1987),232-243.
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##### 出版历程
• 收稿日期:  1990-10-04
• 刊出日期:  1991-12-15

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