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Bifurcations of Double Homoclinic Loops in Reversible Systems
International Journal of Bifurcation and Chaos ( IF 2.2 ) Pub Date : 2020-12-30 , DOI: 10.1142/s0218127420502466 Yuzhen Bai 1 , Xingbo Liu 2
International Journal of Bifurcation and Chaos ( IF 2.2 ) Pub Date : 2020-12-30 , DOI: 10.1142/s0218127420502466 Yuzhen Bai 1 , Xingbo Liu 2
Affiliation
This paper is devoted to the study of bifurcation phenomena of double homoclinic loops in reversible systems. With the aid of a suitable local coordinate system, the Poincaré map is constructed. By means of the bifurcation equation, we perform a detailed study to obtain fruitful results, and demonstrate the existence of the R-symmetric large homoclinic orbit of new type near the primary double homoclinic loops, the existence of infinitely many R-symmetric periodic orbits accumulating onto the R-symmetric large homoclinic orbit, and the coexistence of R-symmetric large homoclinic orbit and the double homoclinic loops. The homoclinic bellow can also be found under suitable perturbation. The relevant bifurcation surfaces and the existence regions are located.
中文翻译:
可逆系统中双同宿环的分岔
本文致力于研究可逆系统中双同宿环的分岔现象。借助合适的局部坐标系,构建庞加莱地图。借助分岔方程,我们进行了详细的研究,取得了丰硕的成果,证明了在主双同宿环附近存在新型R对称大同宿轨道,存在无限多R对称周期轨道累积R对称大同宿轨道,R对称大同宿轨道与双同宿环共存。在适当的扰动下也可以找到同宿波纹管。定位相关的分岔面和存在区域。
更新日期:2020-12-30
中文翻译:
可逆系统中双同宿环的分岔
本文致力于研究可逆系统中双同宿环的分岔现象。借助合适的局部坐标系,构建庞加莱地图。借助分岔方程,我们进行了详细的研究,取得了丰硕的成果,证明了在主双同宿环附近存在新型R对称大同宿轨道,存在无限多R对称周期轨道累积R对称大同宿轨道,R对称大同宿轨道与双同宿环共存。在适当的扰动下也可以找到同宿波纹管。定位相关的分岔面和存在区域。