By using the linear independent fundamental solutions of the linearvariational equation along the heteroclinic loop to establish a suitable local coordinate system insome small tubular neighborhood of the heteroclinic...By using the linear independent fundamental solutions of the linearvariational equation along the heteroclinic loop to establish a suitable local coordinate system insome small tubular neighborhood of the heteroclinic loop, the Poincaré map is constructed to studythe bifurcation problems of a fine 3–point loop in higher dimensional space. Under some transversalconditions and the non–twisted condition, the existence, coexistence and incoexistence of2–point–loop, 1–homoclinic orbit, simple 1–periodic orbit and 2–fold 1–periodic orbit, and thenumber of 1–periodic orbits are studied. Moreover, the bifurcation surfaces and existence regionsare given. Lastly, the above bifurcation results are applied to a planar system and an insidestability criterion is obtained.展开更多
基金This work is supported by the National Natural Science Foundation of China(10371040)the Shanghai Priority Academic Disciplinesthe Scientific Research Foundation of Linyi Teacher's University 37C29,34C23,34C37
文摘By using the linear independent fundamental solutions of the linearvariational equation along the heteroclinic loop to establish a suitable local coordinate system insome small tubular neighborhood of the heteroclinic loop, the Poincaré map is constructed to studythe bifurcation problems of a fine 3–point loop in higher dimensional space. Under some transversalconditions and the non–twisted condition, the existence, coexistence and incoexistence of2–point–loop, 1–homoclinic orbit, simple 1–periodic orbit and 2–fold 1–periodic orbit, and thenumber of 1–periodic orbits are studied. Moreover, the bifurcation surfaces and existence regionsare given. Lastly, the above bifurcation results are applied to a planar system and an insidestability criterion is obtained.
