Codimension 2 bifurcations of double homoclinic loops |
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| Authors: | Weipeng Zhang Deming Zhu |
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| Affiliation: | 1. Department of Basic Science, Faculty of Computers and Informatics, Suez Canal University, Ismailia 41522, Egypt;2. Department of Engineering Mathematics and Physics, Faculty of Engineering, Mansoura University, Mansoura 35516, Egypt;3. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt;1. Department of Applied Mathematics, Shanghai Institute of Technology, Shanghai 201418, China;2. Department of Mathematics, East China Normal University, Shanghai 200241, China;3. Division of Computational Science, E-Institute of Shanghai Universities at SJTU, Shanghai 200030;1. Department of Mathematical Sciences, Clemson University, South Carolina, United States;2. School of Human Evolution and Social Change; Simon A. Levin Mathematical Computational and Modeling Science Center, Arizona State University, Tempe, Arizona, United States;3. Department of Biostatistics and Informatics, University of Colorado, Denver, Colorado, United States |
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| Abstract: | In this work, the double-homoclinic-loop bifurcations in four dimensional vector fields are investigated by setting up local coordinates near the double homoclinic loops. We get the existence, uniqueness and incoexistence of the large 1-hom and large 1-per orbit, and their corresponding existence regions are located. Furthermore, the inexistence of the large 2-hom and large 2-per orbit are also demonstrated. |
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