Bifurcations of twisted double homoclinic loops with resonant condition
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Authors
Yinlai Jin
- School of Science, Linyi University, Linyi, Shandong, 276005, China.
Man Zhu
- School of Science, Linyi University, Linyi, Shandong, 276005, China.
- School of Mathematical Sciences, Shandong Normal University, Jinan, 250014, China.
Feng Li
- School of Science, Linyi University, Linyi, Shandong, 276005, China.
Dandan Xie
- School of Science, Linyi University, Linyi, Shandong, 276005, China.
- School of Mathematical Sciences, Shandong Normal University, Jinan, 250014, China.
Nana Zhang
- School of Science, Linyi University, Linyi, Shandong, 276005, China.
- School of Mathematical Sciences, Shandong Normal University, Jinan, 250014, China.
Abstract
In this paper, the bifurcation problems of twisted double homoclinic loops with resonant condition
are studied for (m + n)-dimensional nonlinear dynamic systems. In the small tubular neighborhoods of
the homoclinic orbits, the foundational solutions of the linear variational systems are selected as the local
coordinate systems. The Poincaré maps are constructed by using the composition of two maps, one is
in the small tubular neighborhood of the homoclinic orbit, and another is in the small neighborhood of
the equilibrium point of system. By the analysis of bifurcation equations, the existence, uniqueness and
existence regions of the large homoclinic loops, large periodic orbits are obtained, respectively. Moreover,
the corresponding bifurcation diagrams are given.
Share and Cite
ISRP Style
Yinlai Jin, Man Zhu, Feng Li, Dandan Xie, Nana Zhang, Bifurcations of twisted double homoclinic loops with resonant condition, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 10, 5579--5620
AMA Style
Jin Yinlai, Zhu Man, Li Feng, Xie Dandan, Zhang Nana, Bifurcations of twisted double homoclinic loops with resonant condition. J. Nonlinear Sci. Appl. (2016); 9(10):5579--5620
Chicago/Turabian Style
Jin, Yinlai, Zhu, Man, Li, Feng, Xie, Dandan, Zhang, Nana. "Bifurcations of twisted double homoclinic loops with resonant condition." Journal of Nonlinear Sciences and Applications, 9, no. 10 (2016): 5579--5620
Keywords
- Double homoclinic loops
- twisted
- resonance
- bifurcation
- higher dimensional system.
MSC
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