An Envelope Method for Analyzing Sequential Pattern Formation

We examine sequential spatial pattern formation in a tissue interaction model for skin organ morphogenesis. Pattern formation occurs as a front sweeps across the domain leaving in its wake a steady state spatial pattern. Extensive numerical simulations show that these fronts travel with constant wave speed. By considering the envelope of the solution profile we present a novel method of calculating its wave speed. Key words. pattern formation, envelope method, sequential pattern formation, wave speed, tissue interaction AMS subject classifications. 92, 35 PII. S003613999732857X

• Type: Journal
• Year: 2000
• Where: SIAMAM
• Authors: Gerhard C. Cruywagen, James D. Murray, Philip K. Maini
• Keywords: Pattern Formation, SIAMAM 2000, Spatial Pattern, Wave Speed