Mechanisms for propagation failure in discrete reaction-diffusion systems

✍ Scribed by Victoria Booth; Thomas Erneux

• Publisher: Elsevier Science
• Year: 1992
• Tongue: English
• Weight: 149 KB
• Volume: 188
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/0378-4371(92)90267-t

✦ Synopsis

We model a chain of coupled bistable reactors by the discrete Nagumo reaction-diffusion equation: du,,/dt = f(u,,) + d(u, +~ + u,, 1 -2u,,), where f(u~) = u~(u,, -1)(a -u,,) and a, d are parameters. We determine a propagating front initiated by the following boundary and initial conditions: u~ = 1 (t >/0) and u,, = 0 (n/> 2 and t = 0). We show that the front fails to propagate (1) if d is too small (d< d*) or (2) if d = d(n) is not uniformly distributed in the system. We investigate both cases by analyzing the limit a--~0 and d(a)---~O.