Advertisement

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

Convergence of attractors

Abstract

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.

References

  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). https://doi.org/10.1007/BF00713717

Download citation

Key words

  • coupled oscillators system
  • attractor
  • cone
  • horizontal curve