Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Convergence of attractors


The system of coupled oscillators and its time-discretization (with constant stepsize h) are considered in this paper. Under some conditions, it is showed that the discrete systems have one-dimensional global attractors lh converging to l which is the global attractor of continuous system.

This is a preview of subscription content, log in to check access.


  1. [1]

    L. Lorenz, Numerics of invariant manifolds and attractors, inChaotic Numerics, Contemporary Mathematics, 172 (1994), 185–202.

  2. [2]

    Y., Kuramoto,Chemical Oscillations. Waves and Turbulence, Springer-Verlag, New York (1984).

  3. [3]

    P., Kloeden and J., Lorenz, Stable attracting sets in dynamical systems and in their one-step discretizations.SIAM J. Numer. Anal.,23, 5 (1986), 986–995.

  4. [4]

    Qian, Min, Shen, Wenxian and Zhang, Jinvan, Global behavior in the dynamical equation of J-J type,J. Differential Equations.71, 2 (1988), 315–333.

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Wenxin, Q., Zengrong, L. Convergence of attractors. Appl Math Mech 18, 1153–1158 (1997).

Download citation

Key words

  • coupled oscillators system
  • attractor
  • cone
  • horizontal curve