scholarly journals Stability analysis of a Lotka-Volterra type predator-prey system with Allee effect on the predator species

2018 ◽  
Keyword(s):  
Stability Analysis ◽  
Allee Effect ◽  
Volterra Type ◽  
Predator Species ◽  
Predator Prey ◽  
Prey System

scholarly journals Dynamic behaviors of a Lotka-Volterra type predator-prey system with Allee effect on the predator species and density dependent birth rate on the prey species

2019 ◽  
Vol 17 (1) ◽  
pp. 1186-1202 ◽  
Author(s):  
Fengde Chen ◽  
Xinyu Guan ◽  
Xiaoyan Huang ◽  
Hang Deng
Keyword(s):  
Birth Rate ◽  
Allee Effect ◽  
Prey Species ◽  
Positive Equilibrium ◽  
Volterra Type ◽  
Predator Species ◽  
Dynamic Behaviors ◽  
Predator Prey ◽  
Density Dependent ◽  
Prey System

Abstract A Lotka-Volterra type predator-prey system with Allee effect on the predator species and density dependent birth rate on the prey species is proposed and studied. For non-delay case, such topics as the persistent of the system, the local stability property of the equilibria, the global stability of the positive equilibrium are investigated. For the system with infinite delay, by using the iterative method, a set of sufficient conditions which ensure the global attractivity of the positive equilibrium is obtained. By introducing the density dependent birth rate, the dynamic behaviors of the system becomes complicated. The system maybe collapse in the sense that both the species will be driven to extinction, or the two species could be coexist in a stable state. Numeric simulations are carried out to show the feasibility of the main results.

PERMANENCE IN A PERIODIC PREDATOR–PREY SYSTEM WITH PREY DISPERSAL AND PREDATOR DENSITY-INDEPENDENT

2006 ◽  
Vol 14 (04) ◽  
pp. 491-507 ◽  
Author(s):  
LONG ZHANG ◽  
ZHIDONG TENG
Keyword(s):  
Periodic Solution ◽  
Prey Species ◽  
Positive Periodic Solution ◽  
Analytic Method ◽  
Predator Density ◽  
Volterra Type ◽  
Predator Species ◽  
Predator Prey ◽  
Prey System ◽  
Theoretical Results

In this paper, we study two-species predator–prey Lotka–Volterra-type dispersal system with periodic coefficients, in which the prey species can disperse among n-patches, but the predator species which is density-independent is confined to some patches and cannot disperse. By utilizing the analytic method, sufficient and realistic conditions on the boundedness, permanence, extinction, and the existence of positive periodic solution are established. The theoretical results are confirmed by a special example and numerical simulations.

scholarly journals The Influence of Fear Effect to a Discrete-Time Predator-Prey System with Predator Has Other Food Resource

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 865
Author(s):  
Jialin Chen ◽  
Xiaqing He ◽  
Fengde Chen
Keyword(s):  
Discrete Time ◽  
Food Resource ◽  
Sufficient Conditions ◽  
Iteration Scheme ◽  
Predator Species ◽  
Predator Prey ◽  
Interior Equilibrium ◽  
Fear Effect ◽  
Prey System ◽  
Trivial Equilibrium

A discrete-time predator–prey system incorporating fear effect of the prey with the predator has other food resource is proposed in this paper. The trivial equilibrium and the predator free equilibrium are both unstable. A set of sufficient conditions for the global attractivity of prey free equilibrium and interior equilibrium are established by using iteration scheme and the comparison principle of difference equations. Our study shows that due to the fear of predation, the prey species will be driven to extinction while the predator species tends to be stable since it has other food resource, i.e., the prey free equilibrium may be globally stable under some suitable conditions. Numeric simulations are provided to illustrate the feasibility of the main results.

Turing Stability Analysis in a Reaction-Diffusion Predator-Prey System with Fear Effect

2021 ◽  
Author(s):  
Gong Chen ◽  
Min Xiao ◽  
Shi Chen ◽  
Shuai Zhou ◽  
Yunxiang Lu ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Reaction Diffusion ◽  
Predator Prey ◽  
Fear Effect ◽  
Prey System

scholarly journals Stability and Bifurcation in a Predator–Prey Model with the Additive Allee Effect and the Fear Effect

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1280
Author(s):  
Liyun Lai ◽  
Zhenliang Zhu ◽  
Fengde Chen
Keyword(s):  
Allee Effect ◽  
Sufficient Conditions ◽  
Positive Equilibrium ◽  
Predator Species ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Fear Effect ◽  
Prey Model ◽  
Strong Allee Effect ◽  
Theoretical Results

We proposed and analyzed a predator–prey model with both the additive Allee effect and the fear effect in the prey. Firstly, we studied the existence and local stability of equilibria. Some sufficient conditions on the global stability of the positive equilibrium were established by applying the Dulac theorem. Those results indicate that some bifurcations occur. We then confirmed the occurrence of saddle-node bifurcation, transcritical bifurcation, and Hopf bifurcation. Those theoretical results were demonstrated with numerical simulations. In the bifurcation analysis, we only considered the effect of the strong Allee effect. Finally, we found that the stronger the fear effect, the smaller the density of predator species. However, the fear effect has no influence on the final density of the prey.

scholarly journals Hopf bifurcation and stability in a Beddington-DeAngelis predator-prey model with stage structure for predator and time delay incorporating prey refuge

2019 ◽  
Vol 17 (1) ◽  
pp. 141-159 ◽  
Author(s):  
Zaowang Xiao ◽  
Zhong Li ◽  
Zhenliang Zhu ◽  
Fengde Chen
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Sufficient Conditions ◽  
Stage Structure ◽  
Prey Refuge ◽  
Predator Species ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Bifurcation And Stability

Abstract In this paper, we consider a Beddington-DeAngelis predator-prey system with stage structure for predator and time delay incorporating prey refuge. By analyzing the characteristic equations, we study the local stability of the equilibrium of the system. Using the delay as a bifurcation parameter, the model undergoes a Hopf bifurcation at the coexistence equilibrium when the delay crosses some critical values. After that, by constructing a suitable Lyapunov functional, sufficient conditions are derived for the global stability of the system. Finally, the influence of prey refuge on densities of prey species and predator species is discussed.

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