Dynamics of a three-species food chain model with fear effect

Cong, Pingping; Fan, Meng; Zou, Xingfu

doi:10.1016/j.cnsns.2021.105809

Cited by 45 publications

(15 citation statements)

References 38 publications

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“…The dynamic phenomena of ODE predator-prey system considering fear effect include: promoting stability, periodic solution (limit cycle), making chaotic state become stable and so on 1,14,16,18,19,[21][22][23][24][25][26] . However, researches on the change of spatial population dynamics caused by fear effect are still not general.…”

Section: Discussionmentioning

confidence: 99%

“…When infected population increases, the uninfected production decreases Population dynamics and epidemic dynamics models considering fear effect have been widely studied [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] . This paper focus on the influence of fear factor on the pattern formation of host parasite model and the complex dynamic changes.…”

Section: Conditionsmentioning

confidence: 99%

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Pattern formation of parasite-host model induced by fear effect

Ye¹,

Zhao²,

Zhou³

2022

Preprint

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In this paper, based on the epidemiological microparasite model, a parasite-host model is established by considering the fear effect of susceptible individuals on infectors. We ex-Pattern formation of parasite-host model induced by fear effect With the development of reaction-diffusion equation, the research on the pattern formation of population model has been widely concerned. Among them, the research on spatiotemporal dynamics of predator-prey model is particularly rich. Recently, Wang et al. 1 first proposed the mathematical expression of fear effect and considered the fear effect in the traditional predator-prey model. It was found that the addition of fear effect brought complex dynamic phenomena. Since then, many predator-prey models with fear effect have been studied. Considering that the fear effect also exists between uninfected host and infected host. Therefore, this paper attempts to introduce the fear effect into the epidemiological microparasite model and construct a parasite-host model with fear effect. With the help of computer, we simulate the distribution of population under different degrees of fear, and combined with other ecological factors to explore how the distribution of population will change under the interference of various factors. Our results show that the growth of pattern satisfies some laws under different ecological factors. Hopefully, this work will provide us further understanding of population dynamics in a real environment stimulated by the fear effect.

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Section: Discussionmentioning

confidence: 99%

Section: Conditionsmentioning

confidence: 99%

Pattern formation of parasite-host model induced by fear effect

Ye¹,

Zhao²,

Zhou³

2022

Preprint

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“…In addition, Sarkara and Khajanchi [23] proposed a predator-prey system introducing the cost of fear into prey reproduction with Holling type-II functional response, which found that the sensitivity of prey to perceive the risk of predation increases with the growth rate of prey or the decay rate of predator. And there are other papers that also consider the influence on the fear effect on the predator-prey models [24][25][26][27][28][29][30][31][32][33]. The above analysis shows that the fear effect and hunting cooperation have a fundamental impact on the dynamics of the predator system.…”

Section: Introductionmentioning

confidence: 94%

Complex dynamics of a predator-prey model with hunting cooperation-induced fear and diffusion

Meng

Zhang

2022

Preprint

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Hunting cooperation is typical behavior among some large predators that increases the predator's ability to capture prey, and hunting cooperation can induce fear, which reduces the birth rate of prey. Based on this fact, in this paper we propose two predator-prey models with hunting cooperation-induced fear. In the first model, we consider the case without the spatial diffusion of populations: we study the bifurcation of the equilibrium points and their stability. Our study finds that (1) the model admits at most two positive equilibria, and when they exist, the model exhibits bistability structures: either between predator-free equilibrium and periodic solution, or between predator-free equilibrium and unique positive equilibrium. (2) When the model has a unique positive equilibrium, it undergoes the Hopf bifurcation. In addition, we analyze the stability and direction of Hopf bifurcated periodic solution, which shows that low-level fear and high-intensity hunting cooperation can cause Hopf bifurcation. (3) If the two positive equilibria coincide, saddle-node bifurcation and Bogdanov-Takens bifurcation of codimension two may occur. Moreover, if the predator population does not hunt cooperatively, the saddle-node bifurcation and Bogdanov-Takens bifurcation disappear. Our research findings generalize the existing results. For the model with spatial diffusion, we first pay attention to whether the model has Turing instability, which favors the formation of biodiversity. We find that when the ratio of the diffusion rate of prey to the diffusion rate of predator exceeds a certain critical value, Turing instability occurs. In addition, we present the existence of Hopf bifurcation and discuss the stability, direction, and period of spatially homogeneous and inhomogeneous periodic solutions. That shows that diffusion accelerates the occurrence of Hopf bifurcation, which destabilizes the population in advance and turns the number of the population into a periodic oscillating. At last, the theoretical analysis is illustrated by numerical simulations. The results show that populations can exhibit predator extinction, stable coexistence, or oscillatory coexistence under the influence of hunting cooperation, fear, or diffusion.Mathematics Subject Classification 92B05 · 92D25 · 35K57 · 37G15

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confidence: 98%

“…More recent work extends the study of fear effect to food-web systems where more than two trophic levels are incorporated [3,16,17,18,25,26]. In [3], the authors studied a three-species food chain model that includes a bottom prey, a middle predator, and a top predator and showed that the fear effect may drive the transition from chaotic behavior to a stable state for the system. In [25], Wang and Zou analyzed the cascading effect of the fear from the top predator to the bottom prey where there is either one middle predator or two middle predators at different trophic levels.…”

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confidence: 98%

Studying the fear effect in a predator-prey system with apparent competition

Wang

Smit

2023

DCDS-B

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<p style='text-indent:20px;'>Recent experimental evidence shows that the mere presence of predators may largely reduce the reproduction success of prey. The loss of prey's reproduction rate is attributed to the cost of anti-predator defense of prey when the prey perceives predation risks. We propose a predator-prey model where the prey shares a common enemy that leads to apparent competition between the prey and also the cost of anti-predator defense. Analytical results give the persistence conditions for the population densities of the prey and the predator. Numerical simulations demonstrate rich dynamics, such as the bi-stability of an equilibrium and a limit cycle. Results also reveal how the prey and the predator may coexist when the anti-predator defense level varies in prey. A relatively strong anti-predator defense in the prey may drive the population density of the prey to extinction and change the original coexistence of all the prey and the predator where the population densities oscillate periodically. Alternatively, strong anti-predator defense in the prey may facilitate the coexistence of the prey and the predator at a steady state.</p>

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Dynamics of a three-species food chain model with fear effect

Cited by 45 publications

References 38 publications

Pattern formation of parasite-host model induced by fear effect

Pattern formation of parasite-host model induced by fear effect

Complex dynamics of a predator-prey model with hunting cooperation-induced fear and diffusion

Studying the fear effect in a predator-prey system with apparent competition

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