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Numerical Studies of Symmetry-Breaking Bifurcations in Reaction-Diffusion Systems

In: Biomathematics and Related Computational Problems

Author

Listed:
  • K. Duncan

    (Heriot-Watt University, Department of Mathematics)

  • J. C. Eilbeck

    (Heriot-Watt University, Department of Mathematics)

Abstract

Reaction-diffusion systems have often been invoked as a mechanism for the generation of chemical gradients which initiate pattern formation in embryos. We describe how, with the aid of path-following methods and the pseudo-spectral method, the space of steady-state solutions of the equations can be systematically mapped out. The results described for 1-space dimension show some regular features which help elucidate previous observations of spatial period-doubling sequences. The sequences of patterns formed in such systems are to some extent independent of the model and the initial conditions. Some results for the 3-dimensional axially-symmetric case are also presented.

Suggested Citation

  • K. Duncan & J. C. Eilbeck, 1988. "Numerical Studies of Symmetry-Breaking Bifurcations in Reaction-Diffusion Systems," Springer Books, in: Luigi M. Ricciardi (ed.), Biomathematics and Related Computational Problems, pages 439-448, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-2975-3_39
    DOI: 10.1007/978-94-009-2975-3_39
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