Stability switching and chaos in a multiple delayed prey-predator model with fear effect and anti-predator behavior

2021 ◽  
Author(s):  
Balram Dubey ◽  
Sajan ◽  
Ankit Kumar
Keyword(s):  
Fear Effect ◽  
Predator Model ◽  
Predator Behavior

scholarly journals Fear effect in discrete prey-predator model incorporating square root functional response

2021 ◽  
Vol 2 (2) ◽  
pp. 51-57
Author(s):  
P.K. Santra
Keyword(s):  
Functional Response ◽  
Stability Condition ◽  
Discrete Model ◽  
Dynamical Behavior ◽  
Phase Portraits ◽  
Square Root ◽  
Bifurcation Diagrams ◽  
Fear Effect ◽  
Hypothetical Data ◽  
Predator Model

In this work, an interaction between prey and its predator involving the effect of fear in presence of the predator and the square root functional response is investigated. Fixed points and their stability condition are calculated. The conditions for the occurrence of some phenomena namely Neimark-Sacker, Flip, and Fold bifurcations are given. Base on some hypothetical data, the numerical simulations consist of phase portraits and bifurcation diagrams are demonstrated to picturise the dynamical behavior. It is also shown numerically that rich dynamics are obtained by the discrete model as the effect of fear.

Stability and Hopf Bifurcation in a Predator–Prey Model with the Cost of Anti-Predator Behaviors

2019 ◽  
Vol 29 (13) ◽  
pp. 1950185 ◽  
Author(s):  
Ting Qiao ◽  
Yongli Cai ◽  
Shengmao Fu ◽  
Weiming wang
Keyword(s):  
Hopf Bifurcation ◽  
Limit Cycle Oscillation ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Fear Effect ◽  
Existence And Stability ◽  
Cycle Oscillation ◽  
Predator Model ◽  
The Stability ◽  
The Cost

In this paper, we investigate the influence of anti-predator behavior in prey due to the fear of predators with a Beddington–DeAngelis prey–predator model analytically and numerically. We give the existence and stability of equilibria of the model, and provide the existence of Hopf bifurcation. In addition, we investigate the influence of the fear effect on the population dynamics of the model and find that the fear effect can not only reduce the population density of both predator and prey, but also prevent the occurrence of limit cycle oscillation and increase the stability of the system.

scholarly journals Impact of the fear and Allee effect on a Holling type II prey–predator model

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Binfeng Xie
Keyword(s):  
Hopf Bifurcation ◽  
Allee Effect ◽  
Jacobian Matrix ◽  
Positive Equilibrium ◽  
Type Ii ◽  
Bifurcation Parameter ◽  
Fear Effect ◽  
Predator Model ◽  
The Stability ◽  
Theoretical Results

AbstractIn this paper, we propose and investigate a prey–predator model with Holling type II response function incorporating Allee and fear effect in the prey. First of all, we obtain all possible equilibria of the model and discuss their stability by analyzing the eigenvalues of Jacobian matrix around the equilibria. Secondly, it can be observed that the model undergoes Hopf bifurcation at the positive equilibrium by taking the level of fear as bifurcation parameter. Moreover, through the analysis of Allee and fear effect, we find that: (i) the fear effect can enhance the stability of the positive equilibrium of the system by excluding periodic solutions; (ii) increasing the level of fear and Allee can reduce the final number of predators; (iii) the Allee effect also has important influence on the permanence of the predator. Finally, numerical simulations are provided to check the validity of the theoretical results.

Impact of the fear effect in a prey-predator model incorporating a prey refuge

2019 ◽  
Vol 356 ◽  
pp. 328-337 ◽  
Author(s):  
Huisen Zhang ◽  
Yongli Cai ◽  
Shengmao Fu ◽  
Weiming Wang
Keyword(s):  
Prey Refuge ◽  
Fear Effect ◽  
Predator Model

scholarly journals Effects of fear and anti-predator response in a discrete system with delay

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Ritwick Banerjee ◽  
Pritha Das ◽  
Debasis Mukherjee
Keyword(s):  
Discrete System ◽  
Prey Species ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
The Other ◽  
Predator Prey ◽  
Predator Response ◽  
Predator Model ◽  
The Cost ◽  
Predator Behavior

<p style='text-indent:20px;'>In this paper a discrete-time two prey one predator model is considered with delay and Holling Type-Ⅲ functional response. The cost of fear of predation and the effect of anti-predator behavior of the prey is incorporated in the model, coupled with inter-specific competition among the prey species and intra-specific competition within the predator. The conditions for existence of the equilibrium points are obtained. We further derive the sufficient conditions for permanence and global stability of the co-existence equilibrium point. It is observed that the effect of fear induces stability in the system by eliminating the periodic solutions. On the other hand the effect of anti-predator behavior plays a major role in de-stabilizing the system by giving rise to predator-prey oscillations. Finally, several numerical simulations are performed which support our analytical findings.</p>

Impact of the Fear Effect on the Stability and Bifurcation of a Leslie–Gower Predator–Prey Model

2020 ◽  
Vol 30 (14) ◽  
pp. 2050210
Author(s):  
Xiaoqin Wang ◽  
Yiping Tan ◽  
Yongli Cai ◽  
Weiming Wang
Keyword(s):  
Limit Cycle ◽  
Limit Cycle Oscillation ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Fear Effect ◽  
Prey Model ◽  
Cycle Oscillation ◽  
The Stability ◽  
Coexistence Equilibrium ◽  
Predator Behavior

In this paper, we investigate analytically and numerically the dynamics of a modified Leslie–Gower predator–prey model which is characterized by the reduction of prey growth rate due to the anti-predator behavior. We prove the existence and local/global stability of equilibria of the model, and verify the existence of Hopf bifurcation. In addition, we focus on the influence of the fear effect on the population dynamics of the model and find that the fear effect can not only reduce the population density of both predator and prey, but also destabilize the coexistence equilibrium, which are beneficial to the occurrence of limit-cycle-induced oscillation, or prevent the occurrence of limit cycle oscillation and increase the stability of the system.

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