Qualitative Analysis for a Kind of Predator-Prey Model of Holling III-Function Response with Nonlinear Density Dependent

2011 ◽  
Author(s):  
Wei-wei Zheng ◽  
Li-gui Luo ◽  
Lei Zhao
Keyword(s):  
Qualitative Analysis ◽  
Predator Prey ◽  
Density Dependent ◽  
Predator Prey Model ◽  
Prey Model

Qualitative analysis of a diffusive Crowley–Martin predator–prey model: the role of nonlinear predator harvesting

2019 ◽  
Vol 98 (2) ◽  
pp. 1169-1189 ◽  
Author(s):  
Vandana Tiwari ◽  
Jai Prakash Tripathi ◽  
Syed Abbas ◽  
Jin-Shan Wang ◽  
Gui-Quan Sun ◽  
...  
Keyword(s):  
Qualitative Analysis ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

Qualitative analysis of a predator–prey model with rapid evolution and piecewise constant arguments

2017 ◽  
Vol 10 (07) ◽  
pp. 1750101 ◽  
Author(s):  
Lie Wang
Keyword(s):  
Qualitative Analysis ◽  
Rapid Evolution ◽  
Flip Bifurcation ◽  
Differential Model ◽  
Piecewise Constant Arguments ◽  
Piecewise Constant ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Linearized Stability

The qualitative analysis of a predator–prey model with rapid evolution and piecewise constant arguments is investigated in this work. The discrete model, which determines the dynamical behavior of the corresponding differential model, is achieved by calculation. First, the sufficient conditions for the existence and local stability of the equilibriums are concluded from the linearized stability theorem and latent root method. Second, the global stability of the equilibriums is discussed through the Poincaré–Bendixson theorem. Furthermore, it is proved that the system has at most one limit cycle. Third, by using the bifurcation theory it is found that the model can undergo the saddle-node bifurcation; the flip bifurcation; and the Neimark–Sacker bifurcation. From the qualitative analysis it can be found that the exponential growth rate and the ratio between the fast and slow timescales have profound influence on the dynamic behavior of the model. Finally, numerical examples carry out to justify the main results in this work.

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