Dynamical study of non-integer order predator–prey system with fear effect

2021 ◽  
pp. 1-9
Author(s):  
Debasis Mukherjee
Keyword(s):  
Dynamical Study ◽  
Predator Prey ◽  
Integer Order ◽  
Fear Effect ◽  
Prey System

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 Dynamics in two competing predators-one prey system with two types of Holling and fear effect

2021 ◽  
Vol 2 (2) ◽  
pp. 58-67
Author(s):  
Adin Lazuardy Firdiansyah ◽  
Nurhidayati Nurhidayati
Keyword(s):  
Consumption Rate ◽  
Numerical Solutions ◽  
Equilibrium Points ◽  
The Other ◽  
Type I ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Fear Effect ◽  
Local Stability Analysis ◽  
Prey System

In this article, it is formulated a predator-prey model of two predators consuming a single limited prey resource. On the other hand, two predators have to compete with each other for survival. The predation function for two predators is assumed to be different where one predator uses Holling type I while the other uses Holling type II. It is also assumed that the fear effect is considered in this model as indirect influence evoked by both predators. Non-negativity and boundedness is written to show the biological justification of the model. Here, it is found that the model has five equilibrium points existed under certain condition. We also perform the local stability analysis on the equilibrium points with three equilibrium points are stable under certain conditions and two equilibrium points are unstable. Hopf bifurcation is obtained by choosing the consumption rate of the second predator as the bifurcation parameter. In the last part, several numerical solutions are given to support the analysis results.

scholarly journals Integrability and Multiple Limit Cycles in a Predator-Prey System with Fear Effect

2019 ◽  
Vol 2019 ◽  
pp. 1-13
Author(s):  
Xinli Li ◽  
Ming Zhang
Keyword(s):  
Limit Cycles ◽  
Positive Equilibrium ◽  
Predator Prey ◽  
Fear Effect ◽  
Prey System ◽  
Integrability Conditions ◽  
Bistable Phenomenon

In this paper, a class of predator-prey systems with fear effect is investigated, the integrability conditions of the origin and the positive equilibrium are obtained, and the fact that three limit cycles can be bifurcated from the positive equilibrium is proved, so bistable phenomenon can occur for this system.

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