|
|||||
 |
|
|
|
|
|
The behavior of
a population interaction-diffusion equation in its
subcritical regime
Mitchell G. Davis, David J. Wollkind, Richard A. Cangelosi and Bonni J. Kealy-Dichone
Vol. 11 (2018), No. 2, 297–309
|
Abstract |
|
A model interaction-diffusion equation for population density originally analyzed through terms of third-order in its supercritical parameter range is extended through terms of fifth-order to examine the behavior in its subcritical regime. It is shown that under the proper conditions the two subcritical cases behave in exactly the same manner as the two supercritical ones unlike the outcome for the truncated system. Further, there also exists a region of metastability allowing for the possibility of population outbreaks. These results are then used to offer an explanation for the occurrence of isolated vegetative patches and sparse homogeneous distributions in the relevant ecological parameter range where there is subcriticality for a plant-groundwater model system, as opposed to periodic patterns and dense homogeneous distributions occurring in its supercritical regime. |
Keywords
interaction-diffusion, Stuart–Watson method, subcritical
bifurcation analysis
|
Mathematical Subject Classification 2010
Primary: 34D20, 35Q56, 92D40
|
Milestones
Received: 15 October 2016
Revised: 27 January 2017
Accepted: 4 February 2017
Published: 17 September 2017
Communicated by Martin J. Bohner
|
Authors |
| Mitchell G. Davis | |
| Department of Mathematics Washington State University Pullman, WA United States |
|
| David J. Wollkind | |
| Department of Mathematics Washington State University Pullman, WA United States |
|
| Richard A. Cangelosi | |
| Department of Mathematics Gonzaga University Spokane, WA United States |
|
| Bonni J. Kealy-Dichone | |
| Department of Mathematics Gonzaga University Spokane, WA United States |
|
|
