吸引子的逼近

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Convergence of Attractors

1.
Department of Mathematics, Suzhou Universitg, Suzhou 215006;
2.
LNM, Institute of Mechanics, Chinese Academy of Science, Beijing, 100080, P. R. China

摘要: 本文考虑耦合振子系统及对其按时间离散化(时间长为h)得到的离散动力系统.证明在一定条件下,这两个系统都有一维整体吸引子l和l_h.进一步证明当时间步长h→0时,l_h→l.
- 耦合振子系 /
- 吸引子 /
- 锥 /
- 水平曲线
Abstract: The system of coupled oscillators and its time-discretization (with constantstepsize h) are considered in this paper. Under some conditions, it is showed that the discrete systems have one-dimensional global attroctors l_h converging to I which is the global attractor of continuous system.
- coupled oscillators system /
- attractor /
- cone /
- horizontat curve

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[3]	P.Kloeden and J.Lorenz.Stable attracting sets in dynamical systems and in their onestep discretizations.SIAM J.Numer.Anal.23.5 (1986).986-995.
[4]	Qian Min.Shen Wenxian and Zhang Jinyan.Global behavior in the dynamical equationof J J type,J.Differential Equations 71.2 (1988),315-333.