A METHOD TO CALCULATE PERIOD DOUBLING BIFURCATION

Applied Mathematics and Mechanics (English Edition) ›› 1987, Vol. 8 ›› Issue (7): 667-671.

A METHOD TO CALCULATE PERIOD DOUBLING BIFURCATION

刘曾荣, 周士刚, 刘尔宁

Anhui University, Hefei

收稿日期:1986-04-10 出版日期:1987-07-18 发布日期:1987-07-18

A METHOD TO CALCULATE PERIOD DOUBLING BIFURCATION

Liu Zheng-rong, Zhou Shi-gang, Liu Er-ning

Anhui University, Hefei

Received:1986-04-10 Online:1987-07-18 Published:1987-07-18

摘要/Abstract

摘要： Based on physical meaning of Melnikov function, we establish a method to calculate period doubling bifurcation and discuss this kind of bifurcation of soft spring Duffing system and find that the result is analogous to subharmonic bifurcation, that is, period doubling bifurcation will appear if damping is small and amplitude of excitation is big. This coincides with facts of physics.

关键词: multiplex eigenvalue, eigenvector, eigenvector chain, Jordan canonical form

Abstract: Based on physical meaning of Melnikov function, we establish a method to calculate period doubling bifurcation and discuss this kind of bifurcation of soft spring Duffing system and find that the result is analogous to subharmonic bifurcation, that is, period doubling bifurcation will appear if damping is small and amplitude of excitation is big. This coincides with facts of physics.

Key words: multiplex eigenvalue, eigenvector, eigenvector chain, Jordan canonical form

刘曾荣;周士刚;刘尔宁. A METHOD TO CALCULATE PERIOD DOUBLING BIFURCATION[J]. Applied Mathematics and Mechanics (English Edition), 1987, 8(7): 667-671.

Liu Zheng-rong;Zhou Shi-gang;Liu Er-ning. A METHOD TO CALCULATE PERIOD DOUBLING BIFURCATION[J]. Applied Mathematics and Mechanics (English Edition), 1987, 8(7): 667-671.

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A METHOD TO CALCULATE PERIOD DOUBLING BIFURCATION

A METHOD TO CALCULATE PERIOD DOUBLING BIFURCATION

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