Abstract
In this paper we formulate a multi-patch multi-species model in which the percapita 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.
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Huang, Y., Diekmann, O. Interspecific influence on mobility and Turing instability. Bull. Math. Biol. 65, 143–156 (2003). https://doi.org/10.1006/bulm.2002.0328
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DOI: https://doi.org/10.1006/bulm.2002.0328