Skip to main content
Log in

Fractal formations in the Lattice Limit Cycle model

  • Statistical and Nonlinear Physics
  • Published:
The European Physical Journal B - Condensed Matter and Complex Systems Aims and scope Submit manuscript

Abstract.

We examine the fractal patterns arising in the Lattice Limit Cycle model, when it is restricted on square and fractal lattices. We show that, for processes taking place on regular 2d substrates, the fractal dimensions depend on the kinetic constants and we have observed a sharp phase-transition from uniform 2d spatial distributions (df=2) when the kinetic parameters are near the Hopf bifurcation point, to a \(d_f \not =2\) inside the limit cycle region. For processes taking place on substrates which contain inactive sites, we observe nucleation of homologous species around inactive regions leading to poisoning, when the active sites are distributed in a fractal manner on the substrate. This is less frequent in cases where the active sites are distributed uniformly and randomly on the lattice leading, normally, to non-trivial steady states.

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

Access this article

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

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. Provata.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tsekouras, G., Provata, A. Fractal formations in the Lattice Limit Cycle model. Eur. Phys. J. B 52, 107–111 (2006). https://doi.org/10.1140/epjb/e2006-00274-x

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjb/e2006-00274-x

PACS.

Navigation