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Singular perturbations of generalized Holling type III predator-prey models with two canard points.
- Source :
-
Journal of Differential Equations . Oct2023, Vol. 371, p116-150. 35p. - Publication Year :
- 2023
-
Abstract
- We study the coexistence of limit cycles in a predator-prey model of Leslie type with generalized Holling type III functional response. When the prey reproduces much faster than the predator, we prove for this model that: (i) the existence of the configuration of one large stable limit cycle enclosing two small unstable limit cycles, (ii) the cyclicity of singular double-head canard cycles is three and reached, and (iii) the coexistence of two stable limit cycles surrounding three equilibria. The last result gives a positive answer to Coleman's problem on the coexistence of two ecologically stable limit cycles in predator-prey models. [ABSTRACT FROM AUTHOR]
- Subjects :
- *SINGULAR perturbations
*LIMIT cycles
*LOTKA-Volterra equations
Subjects
Details
- Language :
- English
- ISSN :
- 00220396
- Volume :
- 371
- Database :
- Academic Search Index
- Journal :
- Journal of Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 167369303
- Full Text :
- https://doi.org/10.1016/j.jde.2023.06.021