Weak type heterodimensional cycle bifurcation with orbit-flip
The paper presents the study of the weak type heterodimensional cycle with orbit-flip in its non-transversal orbit. The main approach is the local moving frame method established in [\textit{D.~Zhu}, ``Problems in homoclinic bifurcation with higher dimensions'', Acta Math. Sin., New Ser. 14, No. 3, 341--352 (1998; Zbl 0932.37032)]. For two subcases, sufficient conditions for the existence, uniqueness and non-coexistence of the homoclinic orbit, heteroclinic orbit and periodic orbit are obtained. Bifurcation surfaces and existence regions are located via bifurcation analysis. For the third subcase, both the coexistence condition for the homoclinic loop and the periodic orbit and the coexistence condition for a persistent heterodimensional cycle and multiple periodic orbits are established. An analytical example is presented to illustrate the main results.
scientific article; zbMATH DE number 5997887
scientific article