Skip to main content
SpringerLink
Log in

Sampling Chaotic Trajectories Quickly in Parallel

  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

The parallel computational complexity of the quadratic map is studied. A parallel algorithm is described that generates typical pseudotrajectories of length t in a time that scales as log t and increases slowly in the accuracy demanded of the pseudotrajectory. Long pseudotrajectories are created in parallel by putting together many short pseudotrajectories; Monte Carlo procedures are used to eliminate the discontinuities between these short pseudotrajectories and then suitably randomize the resulting long pseudotrajectory. Numerical simulations are presented that show the scaling properties of the parallel algorithm. The existence of the fast parallel algorithm provides a way to formalize the intuitive notion that chaotic systems do not generate complex histories.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. H. E. Nusse and J. A. Yorke, Is every approximate trajectory of some process near an exact trajectory of a nearby process? Commun. Math. Phys. 114:363–379 (1988).

    Google Scholar 

  2. R. Greenlaw, H. J. Hoover, and W. L. Ruzzo, Limits to Parallel Computation: P-completeness Theory (Oxford University Press, 1995).

  3. C Dellago, P. G. Bolhuis, F. S. Csajka, and D. Chandler, Transition path sampling and the calculation of rate constants, J. Chem. Phys. 108:1964–1977 (1998).

    Google Scholar 

  4. C. G. Langton, Computation at the edge of chaos, Phys. D 42:12–37 (1990).

    Google Scholar 

  5. K. Moriarty, J. Machta, and R. Greenlaw, Parallel algorithm and dynamic exponent for diffusion-limited aggregation, Phys. Rev. E 55:6211 (1997).

    Google Scholar 

  6. C. Moore and M. Nilsson, The computational complexity of sandpiles, J. Stat. Phys. 96:205–224 (1999).

    Google Scholar 

  7. J. Machta and X.-N. Li, Parallel dynamics and computational complexity of the Bak-Sneppen model, Phys. A 300:245–270 (2001).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, University of Massachusetts, Amherst, Massachusetts, 01003-3720

    J. Machta

Authors
  1. J. Machta
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Machta, J. Sampling Chaotic Trajectories Quickly in Parallel. Journal of Statistical Physics 109, 863–873 (2002). https://doi.org/10.1023/A:1020431119088

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1020431119088

Search

Navigation