Dynamical behavior of a stochastic Nicholson’s blowflies model with distributed delay and degenerate diffusion

2021 ◽  
Author(s):  
Xiaojie Mu ◽  
Daqing Jiang ◽  
Tasawar Hayat ◽  
Ahmed Alsaedi ◽  
Bashir Ahmad
Keyword(s):  
Dynamical Behavior ◽  
Distributed Delay ◽  
Degenerate Diffusion ◽  
Nicholson’S Blowflies Model

scholarly journals Dynamical Behavior and Stability Analysis in a Stage-Structured Prey Predator Model with Discrete Delay and Distributed Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
Chao Liu ◽  
Qingling Zhang
Keyword(s):  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Local Stability ◽  
Dynamical Behavior ◽  
Distributed Delay ◽  
Stable Limit ◽  
Discrete Delay ◽  
Normal Form Theory ◽  
Interior Equilibrium ◽  
Predator Model

We propose a prey predator model with stage structure for prey. A discrete delay and a distributed delay for predator described by an integral with a strong delay kernel are also considered. Existence of two feasible boundary equilibria and a unique interior equilibrium are analytically investigated. By analyzing associated characteristic equation, local stability analysis of boundary equilibrium and interior equilibrium is discussed, respectively. It reveals that interior equilibrium is locally stable when discrete delay is less than a critical value. According to Hopf bifurcation theorem for functional differential equations, it can be found that model undergoes Hopf bifurcation around the interior equilibrium when local stability switch occurs and corresponding stable limit cycle is observed. Furthermore, directions of Hopf bifurcation and stability of the bifurcating periodic solutions are studied based on normal form theory and center manifold theorem. Numerical simulations are carried out to show consistency with theoretical analysis.

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