Interspecific Influence on Mobility and Turing Instability

✍ Scribed by Yunxin Huang; Odo Diekmann

• Book ID: 102567485
• Publisher: Springer
• Year: 2003
• Tongue: English
• Weight: 203 KB
• Volume: 65
• Category: Article
• ISSN: 1522-9602
• DOI: 10.1006/bulm.2002.0328

✦ Synopsis

In this paper we formulate a multi-patch multi-species model in which the per-capita emigration rate of one species depends on the density of some other species. We then focus on Turing instability to examine if and when this cross-emigration response has crucial effects. We find that the type of interaction matters greatly. In the case of competition a cross-emigration response promotes pattern formation by exercising a destabilizing influence; in particular, it may lead to diffusive instability provided that the response is sufficiently strong, which contrasts sharply with the well-known fact that the standard competition system does not exhibit Turing instability. In the case of prey-predator or activator-inhibitor interaction it acts against pattern formation by exerting a stabilizing effect; in particular, the diffusive instability, even though it may happen in a standard system, never occurs when the response is sufficiently strong. We conclude that the cross-emigration response is an important factor that should not be ignored when pattern formation is the issue.