Travelling waves in a tissue interaction model for skin pattern formation

✍ Scribed by G. C. Cruywagen; P. K. Maini; J. D. Murray

• Publisher: Springer
• Year: 1994
• Tongue: English
• Weight: 839 KB
• Volume: 33
• Category: Article
• ISSN: 0303-6812
• DOI: 10.1007/bf00160179

✦ Synopsis

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 a n d that they are in good agreement with our analytical results. Finally, the biological implications of our analysis are discussed.