Bifurcation analysis in a singular Beddington-DeAngelis predator-prey model with two delays and nonlinear predator harvesting.
Math Biosci Eng
; 16(4): 2668-2696, 2019 03 26.
Article
en En
| MEDLINE
| ID: mdl-31137232
ABSTRACT
In this paper, a differential algebraic predator-prey model including two delays, Beddington-DeAngelis functional response and nonlinear predator harvesting is proposed. Without considering time delay, the existence of singularity induced bifurcation is analyzed by regarding economic interest as bifurcation parameter. In order to remove singularity induced bifurcation and stabilize the proposed system, state feedback controllers are designed in the case of zero and positive economic interest respectively. By the corresponding characteristic transcendental equation, the local stability of interior equilibrium and existence of Hopf bifurcation are discussed in the different case of two delays. By using normal form theory and center manifold theorem, properties of Hopf bifurcation are investigated. Numerical simulations are given to demonstrate our theoretical results.
Palabras clave
Texto completo:
1
Colección:
01-internacional
Banco de datos:
MEDLINE
Asunto principal:
Conducta Predatoria
/
Simulación por Computador
/
Dinámica Poblacional
/
Ecosistema
Tipo de estudio:
Prognostic_studies
Límite:
Animals
Idioma:
En
Revista:
Math Biosci Eng
Año:
2019
Tipo del documento:
Article