Dynamics of a 3D autonomous quadratic system with an invariant algebraic surface |
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| Authors: | Zhen Wang Zhouchao Wei Xiaojian Xi Yongxin Li |
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| Institution: | 1. Department of Mathematics, Xijing University, Xi’an?, 710123, People’s Republic of China
2. School of Mathematics and Physics, China University of Geosciences, Wuhan?, 430074, People’s Republic of China
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| Abstract: | An invariant algebraic surface is calculated for a 3D autonomous quadratic system. Also, the dynamics near finite singularities and near infinite singularities on the invariant algebraic surface is analyzed. Furthermore, pitchfork bifurcation is analyzed using center manifold theorem and a first integral of this quadratic system for some special parameters is provided. Finally, the dynamics of this system at infinity using the Poincare compactification in \(R^3\) is investigated and the singularly degenerate heteroclinic cycles are presented by a first integral and verified by numerical simulations. |
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