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Multiplicity and stability of a predator–prey model with non-monotonic conversion rate
- Source :
-
Nonlinear Analysis: Real World Applications . Feb2009, Vol. 10 Issue 1, p154-171. 18p. - Publication Year :
- 2009
-
Abstract
- Abstract: This paper is concerned with a predator–prey model possessing a non-monotonic conversion rate. The main purpose is to determine the multiple existence and stability of positive steady-state solutions to this system. The results show that if the parameter is suitably large, then the system contains an -shaped global bifurcation curve with respect to a bifurcation parameter. That is, the system has two or three positive solutions for a suitable range of parameters. Moreover, the stability of positive solutions on this curve is also given. If is properly small, both uniqueness and non-uniqueness results can occur. The main tools used here include the bifurcation theory, the Lyapunov–Schmidt procedure, and the perturbation technique. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 14681218
- Volume :
- 10
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Nonlinear Analysis: Real World Applications
- Publication Type :
- Academic Journal
- Accession number :
- 34201865
- Full Text :
- https://doi.org/10.1016/j.nonrwa.2007.08.020