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Travelling waves in a tissue interaction model for skin pattern formation

By G. C. Cruywagen, P. K. Maini and J. D. Murray

Abstract

Tissue interaction plays a major role in many morphogenetic processes, particularly those associated with skin organ primordia. We examine travelling wave solutions in a tissue interaction model for skin pattern formation which is firmly based on the known biology. From a phase space analysis we conjecture the existence of travelling waves with specific wave speeds. Subsequently, analytical approximations to the wave profiles are derived using perturbation methods. We then show numerically that such travelling wave solutions do exist and that they are in good agreement with our analytical results. Finally, the biological implications of our analysis are discussed

Topics: Biology and other natural sciences
Year: 1994
DOI identifier: 10.1007/BF00160179
OAI identifier: oai:generic.eprints.org:490/core69

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Citations

  1. (1937). Analysis of wave phenomena in a morphogenetic mechanochemical model and an application to post-fertilisation waves on eggs. doi
  2. (1992). Bifurcating spatial patterns arising from travelling waves in a tissue interaction model. doi
  3. (1987). J.-P.: Cortical activity in vertebrate eggs. I. The activation waves. doi

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