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Bifurcation Analysis of a Predator–Prey Model with Age Structure.
- Source :
- International Journal of Bifurcation & Chaos in Applied Sciences & Engineering; Jun2020, Vol. 30 Issue 8, pN.PAG-N.PAG, 30p
- Publication Year :
- 2020
-
Abstract
- In this paper, a predator–prey model with age structure in predator is studied. Using maturation period as the varying parameter, we prove the existence of Hopf bifurcation for the model and calculate the bifurcation properties, such as the direction of Hopf bifurcation and the stability of bifurcated periodic solutions. The method we employed includes Hopf bifurcation theorem, center manifolds and normal form theory for the abstract Cauchy problems with nondense domain. Under a certain set of parameter values, it turns out that subcritical Hopf bifurcation may occur, indicating that the increment of maturation period could stabilize the steady state, which is initially unstable and enclosed by a stable periodic solution. In addition, stability switches will also take place. Numerical simulations are finally carried out to show the theoretical results. [ABSTRACT FROM AUTHOR]
- Subjects :
- HOPF bifurcations
CAUCHY problem
MANIFOLDS (Mathematics)
COMPUTER simulation
AGE
Subjects
Details
- Language :
- English
- ISSN :
- 02181274
- Volume :
- 30
- Issue :
- 8
- Database :
- Complementary Index
- Journal :
- International Journal of Bifurcation & Chaos in Applied Sciences & Engineering
- Publication Type :
- Academic Journal
- Accession number :
- 144542896
- Full Text :
- https://doi.org/10.1142/S021812742050114X