The Shilnikov type homoclinic orbits of perturbed cubic polynomial Moon-Rand systems
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Authors
Dandan Xie
- School of Mathematics and Statistics, Linyi University, Linyi, Shandong, 276005, P. R. China.
Yinlai Jin
- School of Mathematics and Statistics, Linyi University, Linyi, Shandong, 276005, P. R. China.
Feng Li
- School of Mathematics and Statistics, Linyi University, Linyi, Shandong, 276005, P. R. China.
Nana Zhang
- School of Mathematics and Statistics, Shandong Normal University, Jinan, Shandong, 250014, P. R. China.
Abstract
In this paper, perturbed polynomial Moon-Rand systems are considered. The Padé approximant and analytic solution in
the neighborhood of the initial value are introduced into the process of constructing the Shilnikov type homoclinic orbits for
three dimensional nonlinear dynamical systems. In order to get real bifurcation parameters, four undetermined coefficients
are introduced including three initial values about position and the value of bifurcation parameter. By the eigenvectors of its
all eigenvalues, the value of the bifurcation parameter and three initial values about position are obtained directly. And, the
analytical expressions of the Shilnikov type homoclinic orbits are achieved and the deletion errors relative to the practical system
are given. In the end, we roughly predict when the horseshoe chaos occurs.
Share and Cite
ISRP Style
Dandan Xie, Yinlai Jin, Feng Li, Nana Zhang, The Shilnikov type homoclinic orbits of perturbed cubic polynomial Moon-Rand systems, Journal of Mathematics and Computer Science, 17 (2017), no. 3, 408-419
AMA Style
Xie Dandan, Jin Yinlai, Li Feng, Zhang Nana, The Shilnikov type homoclinic orbits of perturbed cubic polynomial Moon-Rand systems. J Math Comput SCI-JM. (2017); 17(3):408-419
Chicago/Turabian Style
Xie, Dandan, Jin, Yinlai, Li, Feng, Zhang, Nana. "The Shilnikov type homoclinic orbits of perturbed cubic polynomial Moon-Rand systems." Journal of Mathematics and Computer Science, 17, no. 3 (2017): 408-419
Keywords
- Pad´e approximant
- analytic solution
- Shilnikov theorem
- homoclinic orbit.
MSC
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