scholarly journals The Effects of Harvesting on the Dynamics of a Leslie–Gower Model

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Jingli Xie ◽  
Hanyan Liu ◽  
Danfeng Luo
Keyword(s):  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Numerical Simulations ◽  
Bifurcation Analysis ◽  
Stable Limit Cycle ◽  
Local Bifurcation ◽  
Stable Limit ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Local Bifurcation Analysis

In this paper, we study a Leslie–Gower predator-prey model with harvesting effects. We carry out local bifurcation analysis and stability analysis. Under certain conditions, the model is shown to undergo a supercritical Hopf bifurcation resulting in a stable limit cycle. Numerical simulations are presented to illustrate our theoretic results.

Bifurcation of Codimension 3 in a Predator–Prey System of Leslie Type with Simplified Holling Type IV Functional Response

2016 ◽  
Vol 26 (02) ◽  
pp. 1650034 ◽  
Author(s):  
Jicai Huang ◽  
Xiaojing Xia ◽  
Xinan Zhang ◽  
Shigui Ruan
Keyword(s):  
Functional Response ◽  
Limit Cycle ◽  
Stable Limit Cycle ◽  
Positive Equilibrium ◽  
Stable Limit ◽  
Homoclinic Loop ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Type Iv ◽  
Stable Equilibria

It was shown in [Li & Xiao, 2007] that in a predator–prey model of Leslie type with simplified Holling type IV functional response some complex bifurcations can occur simultaneously for some values of parameters, such as codimension 1 subcritical Hopf bifurcation and codimension 2 Bogdanov–Takens bifurcation. In this paper, we show that for the same model there exists a unique degenerate positive equilibrium which is a degenerate Bogdanov–Takens singularity (focus case) of codimension 3 for other values of parameters. We prove that the model exhibits degenerate focus type Bogdanov–Takens bifurcation of codimension 3 around the unique degenerate positive equilibrium. Numerical simulations, including the coexistence of three hyperbolic positive equilibria, two limit cycles, bistability states (one stable equilibrium and one stable limit cycle, or two stable equilibria), tristability states (two stable equilibria and one stable limit cycle), a stable limit cycle enclosing a homoclinic loop, a homoclinic loop enclosing an unstable limit cycle, or a stable limit cycle enclosing three unstable hyperbolic positive equilibria for various parameter values, confirm the theoretical results.

Turing–Hopf bifurcation analysis of a predator–prey model with herd behavior and cross-diffusion

2016 ◽  
Vol 86 (1) ◽  
pp. 73-89 ◽  
Author(s):  
Xiaosong Tang ◽  
Yongli Song ◽  
Tonghua Zhang
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Analysis ◽  
Herd Behavior ◽  
Predator Prey ◽  
Cross Diffusion ◽  
Predator Prey Model ◽  
Prey Model

Stability and Hopf bifurcation analysis of a predator-prey model with time delayed incomplete trophic transfer

2015 ◽  
Vol 31 (1) ◽  
pp. 235-246 ◽  
Author(s):  
Chang-qin Zhang ◽  
Liping Liu ◽  
Ping Yan ◽  
Lin-zhong Zhang
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation Analysis ◽  
Trophic Transfer ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

Stability and Hopf bifurcation analysis of a diffusive predator–prey model with Smith growth

2015 ◽  
Vol 08 (01) ◽  
pp. 1550013 ◽  
Author(s):  
M. Sivakumar ◽  
M. Sambath ◽  
K. Balachandran
Keyword(s):  
Boundary Condition ◽  
Hopf Bifurcation ◽  
Bifurcation Analysis ◽  
Neumann Boundary Condition ◽  
Local Stability ◽  
Neumann Boundary ◽  
Turing Instability ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

In this paper, we consider a diffusive Holling–Tanner predator–prey model with Smith growth subject to Neumann boundary condition. We analyze the local stability, existence of a Hopf bifurcation at the co-existence of the equilibrium and stability of bifurcating periodic solutions of the system in the absence of diffusion. Furthermore the Turing instability and Hopf bifurcation analysis of the system with diffusion are studied. Finally numerical simulations are given to demonstrate the effectiveness of the theoretical analysis.

scholarly journals Stability Analysis and Hopf Bifurcation for ODE System of Predator-Prey Model with Mutual Interference

2021 ◽  
Vol 12 (09) ◽  
pp. 793-802
Author(s):  
Khalid Ahmed Abbakar ◽  
Yafei Yang ◽  
Alhussein Mohamed ◽  
Songchen Xia ◽  
Mogahid Mamoon Abkar ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Mutual Interference ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Ode System ◽  
Prey Model
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