Effects of fear in a fractional-order predator-prey system with predator density-dependent prey mortality

2021 ◽  
Vol 145 ◽  
pp. 110711
Author(s):  
Fatma Bozkurt Yousef ◽  
Ali Yousef ◽  
Chandan Maji
Keyword(s):  
Fractional Order ◽  
Predator Density ◽  
Predator Prey ◽  
Density Dependent ◽  
Prey System

Dynamics of a non-autonomous density-dependent predator–prey model with Beddington–DeAngelis type

2016 ◽  
Vol 09 (04) ◽  
pp. 1650050 ◽  
Author(s):  
Haiyin Li ◽  
Zhikun She
Keyword(s):  
Density Dependence ◽  
Periodic Solutions ◽  
Sufficient Condition ◽  
Positive Periodic Solutions ◽  
Predator Density ◽  
Predator Prey ◽  
Density Dependent ◽  
Predator Prey Model ◽  
Prey System ◽  
Biological Environment

The goal of this paper is to investigate the dynamics of a non-autonomous density-dependent predator–prey system with Beddington–DeAngelis functional response, where not only the prey density dependence but also the predator density dependence are considered, such that the studied predator–prey system conforms to the realistically biological environment. We firstly introduce a sufficient condition for the permanence of the system and then use a specific set to obtain a weaker sufficient condition. Afterward, we provide corresponding conditions for the extinction of the system and the existence of boundary periodical solutions, respectively. Further, we get a sufficient condition for global attractiveness of the boundary periodic solution by constructing a Lyapunov function, arriving at the uniqueness of boundary periodic solutions since the uniqueness of boundary periodic solutions can be ensured by global attractiveness. Finally, based on the existence of positive periodic solutions, which can be ensured by the Brouwer fixed-point theorem, we provide a sufficient condition for the uniqueness of positive periodic solutions.

Dynamic analysis of a fractional order delayed predator–prey system with harvesting

2016 ◽  
Vol 135 (1-2) ◽  
pp. 59-72 ◽  
Author(s):  
Ping Song ◽  
Hongyong Zhao ◽  
Xuebing Zhang
Keyword(s):  
Dynamic Analysis ◽  
Fractional Order ◽  
Predator Prey ◽  
Prey System

Stability and Hopf Bifurcation of a Delayed Density-Dependent Predator–Prey System with Beddington–DeAngelis Functional Response

2016 ◽  
Vol 26 (10) ◽  
pp. 1650165 ◽  
Author(s):  
Haiyin Li ◽  
Gang Meng ◽  
Zhikun She
Keyword(s):  
Hopf Bifurcation ◽  
Density Dependence ◽  
Functional Response ◽  
Positive Equilibrium ◽  
Stability Switches ◽  
Predator Prey ◽  
Geometric Criterion ◽  
Density Dependent ◽  
Prey System ◽  
The Stability

In this paper, we investigate the stability and Hopf bifurcation of a delayed density-dependent predator–prey system with Beddington–DeAngelis functional response, where not only the prey density dependence but also the predator density dependence are considered such that the studied predator–prey system conforms to the realistically biological environment. We start with the geometric criterion introduced by Beretta and Kuang [2002] and then investigate the stability of the positive equilibrium and the stability switches of the system with respect to the delay parameter [Formula: see text]. Especially, we generalize the geometric criterion in [Beretta & Kuang, 2002] by introducing the condition [Formula: see text] which can be assured by the condition [Formula: see text], and adopting the technique of lifting to define the function [Formula: see text] for alternatively determining stability switches at the zeroes of [Formula: see text]s. Afterwards, by the Poincaré normal form for Hopf bifurcation in [Kuznetsov, 1998] and the bifurcation formulae in [Hassard et al., 1981], we qualitatively analyze the properties for the occurring Hopf bifurcations of the system (3). Finally, an example with numerical simulations is given to illustrate the obtained results.

scholarly journals Further Results on Bifurcation for a Fractional-Order Predator-Prey System concerning Mixed Time Delays

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Zhenjiang Yao ◽  
Bingnan Tang
Keyword(s):  
Fractional Order ◽  
Time Delays ◽  
Bifurcation Theory ◽  
Predator Prey ◽  
Mixed Time Delays ◽  
Predator Prey Model ◽  
Prey System ◽  
Change Of Variable ◽  
Set Up ◽  
The Stability

In the present work, we mainly focus on a new established fractional-order predator-prey system concerning both types of time delays. Exploiting an advisable change of variable, we set up an isovalent fractional-order predator-prey model concerning a single delay. Taking advantage of the stability criterion and bifurcation theory of fractional-order dynamical system and regarding time delay as bifurcation parameter, we establish a new delay-independent stability and bifurcation criterion for the involved fractional-order predator-prey system. The numerical simulation figures and bifurcation plots successfully support the correctness of the established key conclusions.

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