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 -