Stability and Hopf bifurcation of a delayed-diffusive predator–prey model with hyperbolic mortality and nonlinear prey harvesting

In this paper, a delayed-diffusive predator–prey model with hyperbolic mortality and nonlinear prey harvesting subject to the homogeneous Neumann boundary conditions is investigated. Firstly, the global asymptotic stability of the unique positive constant equilibrium is obtained by an iteration tech...

Full description

Saved in:
Bibliographic Details
Published inNonlinear dynamics Vol. 88; no. 2; pp. 1397 - 1412
Main Authors Zhang, Fengrong, Li, Yan
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.04.2017
Springer Nature B.V
Subjects
Automotive Engineering
Bifurcation theory
Boundary conditions
Canonical forms
Classical Mechanics
Computer simulation
Control
Dynamical Systems
Engineering
Existence theorems
Hopf bifurcation
Iterative methods
Mathematical models
Mechanical Engineering
Mortality
Original Paper
Predator-prey simulation
Stability
Time lag
Vibration
Stability
34C23
35B35
35B32
Hopf bifurcation
Predator–prey model
92D40
Delay
Reaction–diffusion
Online AccessGet full text

Cover

More Information
Summary:In this paper, a delayed-diffusive predator–prey model with hyperbolic mortality and nonlinear prey harvesting subject to the homogeneous Neumann boundary conditions is investigated. Firstly, the global asymptotic stability of the unique positive constant equilibrium is obtained by an iteration technique. Secondly, regarding time delay as a bifurcation parameter and using the normal form theory and center manifold theorem, the existence, stability and direction of bifurcating periodic solutions are demonstrated, respectively. Finally, numerical simulations are conducted to illustrate the theoretical analysis.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-016-3318-8