Bifurcations of resonant double homoclinic loops for higher dimensional systems


Authors

Yinlai Jin - School of Science, Linyi University, Linyi, Shandong, 276005, P. R. China. Han Xu - School of Science, Linyi University, Linyi, Shandong, 276005, P. R. China. Yuerang Gao - School of Science, Linyi University, Linyi, Shandong, 276005, P. R. China. Xue Zhao - School of Science, Linyi University, Linyi, Shandong, 276005, P. R. China. Dandan Xie - School of Science, Linyi University, Linyi, Shandong, 276005, P. R. China.


Abstract

In this work, we study the bifurcation problems of double homoclinic loops with resonant condition for higher dimensional systems. The Poincaré maps are constructed by using the foundational solutions of the linear variational systems as the local coordinate systems in the small tubular neighborhoods of the homoclinic orbits. We obtain the existence, number and existence regions of the small homoclinic loops, small periodic orbits, and the large homoclinic loops, large periodic orbits, respectively. Moreover, the complete bifurcation diagrams are given.


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