Bifurcations of twisted double homoclinic loops with resonant condition


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.


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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


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