A new algorithm for computation of two-dimensional unstable manifolds and its applications
Qingdu Li, Xiao‐Song Yang, (1)重庆邮电大学系统科学研究中心非线性系统研究所，重庆 400065; (2)重庆邮电大学系统科学研究中心非线性系统研究所，重庆 400065；华中科技大学数学系，武汉 430074 · Acta Physica Sinica · 2010
This paper proposes a new algorithm for computing two-dimensional （un）stable manifolds in time continuous systems. With this algorithm, one can not only get a picture of a manifold efficiently, but also has many information of its every point, which are very useful for investigating the global dynamics of a system geometrically, such as features of stability region, evolution of the system flow and so on. The algorithm is mainly by finding many well distributed trajectories by solving initial value problems. An example on Lorenz system suggests this algorithm is very convenient. In addition, we study the chaotic dynamic of a three-dimensional neural network by detecting a heteroclinic orbit.