TY - JOUR AU - Xie, Dandan AU - Jin, Yinlai AU - Li, Feng AU - Zhang, Nana PY - 2017 TI - The Shilnikov type homoclinic orbits of perturbed cubic polynomial Moon-Rand systems JO - Journal of Mathematics and Computer Science SP - 408-419 VL - 17 IS - 3 AB - 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. SN - ISSN 2008-949X UR - http://dx.doi.org/10.22436/jmcs.017.03.06 DO - 10.22436/jmcs.017.03.06 ID - Xie2017 ER - TY - JOUR TI - Study of two-Dimensional axisymmetric breathers using Padé approximants AU - E. Emaci AU - A. F. Vakakis AU - I. V. Andrianov AU - Y. Mikhlin JO - Nonlinear Dynam. PY - 1997 DA - 1997// VL - 13 ID - Emaci1997 ER - TY - JOUR TI - The construction of homoclinic and heteroclinic orbitals in asymmetric strongly nonlinear systems based on the Padé approximant AU - J. J. Feng AU - Q. C. Zhang AU - W. Wang JO - Chinese Physics B PY - 2011 DA - 2011// VL - 20 ID - Feng2011 ER - TY - JOUR TI - Chaos of several typical asymmetric systems AU - J. J. Feng AU - Q. C. Zhang AU - W. Wang JO - Chaos Solitons and Fractals PY - 2012 DA - 2012// VL - 45 ID - Feng2012 ER - TY - JOUR TI - Homoclinic orbits in three-dimensional Shilnikov-type chaotic systems AU - J. J. Feng AU - Q. C. Zhang AU - W. Wang AU - S. Y. Hao JO - Chinese Physics B, PY - 2013 DA - 2013// VL - 22 ID - Feng2013 ER - TY - JOUR TI - n-Dimensional stable and unstable manifolds of hyperbolic singular point AU - Y. H. Li AU - S. M. Zhu JO - Chaos Solitons Fractals PY - 2006 DA - 2006// VL - 29 ID - Li2006 ER - TY - JOUR TI - The construction of homo-and heteroclinic orbits in non-linear systems AU - G. V. Manucharyan AU - Y. V. Mikhlin JO - J. Appl. Math. Mech. PY - 2005 DA - 2005// VL - 69 ID - Manucharyan2005 ER - TY - JOUR TI - Matching of local expansions in the theory of non-linear vibrations AU - Y. V. Mikhlin JO - J. Sound Vibration PY - 1995 DA - 1995// VL - 182 ID - Mikhlin1995 ER - TY - JOUR TI - Analytical construction of homoclinic orbits of two-and three-dimensional Dynamical Systems AU - Y. V. Mikhlin JO - J. Sound Vibration PY - 2000 DA - 2000// VL - 230 ID - Mikhlin2000 ER - TY - JOUR TI - Analytic approximation of the homoclinic orbits of the lorenz system at \(\sigma= 10, b = 8/3\) and \(\rho= 13.926 . . .\) AU - A. F. Vakakis AU - M. F. A. Azeez JO - Nonlinear Dynam. PY - 1998 DA - 1998// VL - 15 ID - Vakakis1998 ER - TY - JOUR TI - Shilnikov sense chaos in a simple three dimensional system AU - W. Wang AU - Q. C. Zhang AU - R. L. Tian JO - Chinese Physics B PY - 2010 DA - 2010// VL - 19 ID - Wang2010 ER -