In this paper, we study the weak type heterodimensional cycle with orbit-flip in its non-transversal orbit by using the local moving frame approach. For the first two subcases, we present the sufficient conditions for...In this paper, we study the weak type heterodimensional cycle with orbit-flip in its non-transversal orbit by using the local moving frame approach. For the first two subcases, we present the sufficient conditions for the existence, uniqueness and non-coexistence of the homoclinic orbit, heteroclinic orbit and periodic orbit. Based on the bifurcation analysis, the bifurcation surfaces and the existence regions are located. And for the third subcase, we theoretically established both the coexistence condition for the homoclinic loop and the periodic orbit and the coexistence condition for the persistent heterodimensional cycle and multiple periodic orbits due to the weak type of the transversal heteroclinic orbit. Moreover, an analytical example is presented for this subcase.展开更多
基金supported by the Foundation of Zhejiang Sci-Tech University (ZSTU)(Grant No. 11432732611046)National Natural Science Foundation of China (Grant No. 10671069)
文摘In this paper, we study the weak type heterodimensional cycle with orbit-flip in its non-transversal orbit by using the local moving frame approach. For the first two subcases, we present the sufficient conditions for the existence, uniqueness and non-coexistence of the homoclinic orbit, heteroclinic orbit and periodic orbit. Based on the bifurcation analysis, the bifurcation surfaces and the existence regions are located. And for the third subcase, we theoretically established both the coexistence condition for the homoclinic loop and the periodic orbit and the coexistence condition for the persistent heterodimensional cycle and multiple periodic orbits due to the weak type of the transversal heteroclinic orbit. Moreover, an analytical example is presented for this subcase.
