Applied Mathematics and Mechanics (English Edition) ›› 2004, Vol. 25 ›› Issue (10): 1176-1183.

• Articles • Previous Articles     Next Articles

TWISTED BIFURCATIONS AND STABILITY OF HOMOCLINIC LOOP WITH HIGHER DIMENSIONS

JIN Yin-lai1,2, ZHU De-ming2   

  1. 1. Department of Mathematics, Linyi Teachers’ University, Linyi, Shandong 276005, P.R.China;
    2. Department of Mathematics, East China Normal University, Shanghai 200062, P.R.China
  • Received:2002-06-18 Revised:2004-03-16 Online:2004-10-18 Published:2004-10-18
  • Supported by:

    the National Natural Science Foundation of China(10371040)

Abstract: By using the linear independent solutions of the linear variational equation along the homoclinic loop as the demanded local coordinates to construct the Poincar? map,the bifurcations of twisted homoclinic loop for higher dimensional systems are studied.Under the nonresonant and resonant conditions,the existence,number and existence regions of the 1-homoclinic loop,1-periodic orbit,2-homoclinic loop,2-periodic orbit and 2-fold 2-periodic orbit were obtained.Particularly,the asymptotic repressions of related bifurcation surfaces were also given.Moreover, the stability of homoclinic loop for higher dimensional systems and nontwisted homoclinic loop for planar systems were studied.

Key words: local coordinate, Poincar? map, twisted bifurcation, 1-periodic orbit, 2-periodic orbit, stability

2010 MSC Number: 

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