Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-24T09:41:09.793Z Has data issue: false hasContentIssue false
  • English
  • Français

Periodic attractors as a result of diffusion

Published online by Cambridge University Press:  19 September 2008

Jan Barkmeijer
Jan Barkmeijer
Affiliation:
Mathematisch Instituut, Postbus 800, 9700 AV Groningen, The Netherlands
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We present a dynamical system in ℝ2 with a global point attractor but so that two such systems, when coupled by linear diffusion, produce a system in ℝ4 with no point attractors and yet with all solutions bounded in the positive time direction.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 7 , Issue 3 , September 1987 , pp. 319 - 335
Copyright
Copyright © Cambridge University Press 1987

References

REFERENCES

[1]Alexander, J. C.. Spontaneous oscillations in two 2-component cells coupled by diffusion. J. Math. Biol. (1986) 23, 205–219.CrossRefGoogle ScholarPubMed
[2]Bar-Eli, K.. On the stability of coupled chemical oscillators. Physica 14D (1985), 242–252.Google Scholar
[3]Howard, L. N.. Nonlinear oscillations in biology. In Lectures in Applied Mathematics, vol. 17, (Hoppensteadt, Frank C. (Ed.)). Amer. Math. Soc., Providence, R.I., 1979, pp 1–67.Google Scholar
[4]Schreiber, I. & Marek, M.. Strange attractors in coupled reaction-diffusion cells. Physica 5D (1982), 258–272.Google Scholar
[5]Smale, S.. A mathematical model of two cells via Turing's equation. In The Hopf bifurcation and its applications. Marsden, J. E. and McCracken, M., Applied Math. Sci., vol. 19 Springer-Verlag, New York, 1976, pp 354–367.CrossRefGoogle Scholar
[6]Turing, A. M.. The chemical basis of morphogenesis, Philos. Trans. Royal Soc. London Ser. B 237 (1952), 37–72.Google Scholar