Modelling the fear effect in a two-species predator–prey system under the influence of toxic substances

Das, Amartya; Samanta, G. P.

doi:10.1007/s12215-020-00570-x

Cited by 24 publications

(6 citation statements)

References 42 publications

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“…In addition, by implicit function theorem, one obtains a curve of (W(𝜛), d v (𝜛), s(𝜛)) of ℌ(W, s, d v ; 𝜛) = 0 in small neighborhood of 𝜛 0 , where 𝜛 0 is any constant satisfying (17), and W(𝜛), s(𝜛), d v (𝜛) are continuously differentiable functions satisfying…”

Section: Conflict Of Interestsmentioning

confidence: 99%

“…Therefore, we shall mainly discuss the effect of indirect factors on predator-prey model. In fact, indirect factors of predator on prey, such as prey refuge (see references [7][8][9][10][11][12] ) and fear effect (see references [10][11][12][13][14][15][16][17][18][19][20] ), have been more frequently studied in recent decades. As we know, prey refuge is a self-protection measure taken by prey, which can effectively avoid the risk of being preyed on by predators and improve the survival rate of prey populations.…”

Section: Introductionmentioning

confidence: 99%

“…1 𝜎 i 𝜇 i cos 𝜛 0 + s𝔪 3 𝔥 5 sin 𝜛 0 cos 𝜛 0 + s𝔪 4 𝔥 6 sin 𝜛 0 cos 𝜛 0 ,𝔭 2 = −d v 𝔥 2 𝜎 𝑗 𝜇 𝑗 sin 𝜛 0 + s𝔪 1 𝔥 3 cos 2 𝜛 0 + s𝔪 2 𝔥 4 cos 2 𝜛 0 , ( ū, v) T = ℨ 2 .Using assumption(17) again for 𝑗 = 2i, we obtain that s = s and d v = dv wheres = 𝔭 2 𝔥 1 𝜎 i 𝜇 i cos 𝜛 0 − 𝔭 1 𝔥 2 𝜎 𝑗 𝜇 𝑗 sin 𝜛 0 𝔥 1 𝜎 i 𝜇 i (𝔪 1 𝔥 3 + 𝔪 2 𝔥 4 )cos 3 𝜛 0 − 𝔥 2 𝜎 𝑗 𝜇 𝑗 (𝔪 3 𝔥 5 + 𝔪 4 𝔥 6 )sin 2 𝜛 0 cos 𝜛 0 , dv = 𝔭 2 (𝔪 3 𝔥 5 + 𝔪 4 𝔥 6 ) sin 𝜛 0 − 𝔭 1 (𝔪 1 𝔥 3 + 𝔪 2 𝔥 4 ) cos 𝜛 0 𝔥 1 𝜎 i 𝜇 i (𝔪 1 𝔥 3 + 𝔪 2 𝔥 4 )cos2 𝜛 0 − 𝔥 2 𝜎 𝑗 𝜇 𝑗 (𝔪 3 𝔥 5 + 𝔪 4 𝔥 6 )sin 2 𝜛 0 .…”

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confidence: 99%

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Bifurcation dynamics of a reaction–diffusion predator–prey model with fear effect in a predator‐poisoned environment

Meng

Hayat

et al. 2022

Math Methods in App Sciences

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In this paper, we propose a reaction-diffusion predator-prey model with fear effect under a predator-poisoned environment. First, we analyze the existence and stability of constant positive steady states. Second, taking the cost of minimum fear as the bifurcation parameter, the direction and stability of spatially homogeneous/inhomogeneous periodic solutions are investigated. Then, some properties of nonconstant positive steady states are investigated, such as nonexistence, existence, and steady state bifurcation. Applying the fixed point index theory, the existence of the nonconstant positive steady state is discussed, indicating that the proper diffusion rate of prey and larger diffusion rate of predator are beneficial to survival of populations. Moreover, taking the diffusion rate of predator as the bifurcation parameter, the steady state bifurcations from simple and double eigenvalues are intensively established. At last, the validity of the theoretical analysis is verified by numerical simulations. Biological interpretation reveals that the fear effect and the diffusion rate of populations can lead to the emergence of Hopf and steady state bifurcation, thereby destroying the stability of populations and promoting the benign evolution of populations.

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Section: Conflict Of Interestsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Bifurcation dynamics of a reaction–diffusion predator–prey model with fear effect in a predator‐poisoned environment

Meng

Hayat

et al. 2022

Math Methods in App Sciences

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“…At present, some literatures, such as [3,4,8,11,14,[16][17][18][19][22][23][24][25][26], have studied the effects of toxins on different ecosystem species. [4] indicated that once some external toxic substances directly infected the prey, then the predator consuming polluted prey was indirectly influenced by the toxicant.…”

Section: Introductionmentioning

confidence: 99%

Spatiotemporal dynamics in a toxin-producing predator–prey model with threshold harvesting

Ye¹,

Zhao²,

Wu³

2023

NAMC

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In this paper, we propose a toxin-producing predator–prey model with threshold harvesting and study spatiotemporal dynamics of the model under the homogeneous Neumann boundary conditions. At first, the persistence property of solutions to the system is investigated. Then the explicit requirements for the existence of nonconstant steady state solutions are derived by studying the relevant characteristic equation. These steady states occur from related constant steady states via steady state bifurcation. Throughout the analysis of the amplitude equations of Turing pattern by the multiple scale method, pattern formation can be found. Finally, we display umericalsimulations to verify the theoretical outcomes.

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“…It involves a parameter k denoting the level of fear to represent the antipredator behaviour of the prey. Some research works have already been done on the ecological system under the influence of predation fear felt by prey species [6][7][8][9][10][11][12][13][14][15][16][17]. Moreover, the impact of fear in a two-species predator-prey model with prey refuge was analyzed by many researchers [11,18,19].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a Predator‐Prey Population in the Presence of Resource Subsidy under the Influence of Nonlinear Prey Refuge and Fear Effect

2021

Self Cite

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In this work, our aim is to investigate the impact of a non-Kolmogorov predator-prey-subsidy model incorporating nonlinear prey refuge and the effect of fear with Holling type II functional response. The model arises from the study of a biological system involving arctic foxes (predator), lemmings (prey), and seal carcasses (subsidy). The positivity and asymptotically uniform boundedness of the solutions of the system have been derived. Analytically, we have studied the criteria for the feasibility and stability of different equilibrium points. In addition, we have derived sufficient conditions for the existence of local bifurcations of codimension 1 (transcritical and Hopf bifurcation). It is also observed that there is some time lag between the time of perceiving predator signals through vocal cues and the reduction of prey’s birth rate. So, we have analyzed the dynamical behaviour of the delayed predator-prey-subsidy model. Numerical computations have been performed using MATLAB to validate all the analytical findings. Numerically, it has been observed that the predator, prey, and subsidy can always exist at a nonzero subsidy input rate. But, at a high subsidy input rate, the prey population cannot persist and the predator population has a huge growth due to the availability of food sources.

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Modelling the fear effect in a two-species predator–prey system under the influence of toxic substances

Cited by 24 publications

References 42 publications

Bifurcation dynamics of a reaction–diffusion predator–prey model with fear effect in a predator‐poisoned environment

Bifurcation dynamics of a reaction–diffusion predator–prey model with fear effect in a predator‐poisoned environment

Spatiotemporal dynamics in a toxin-producing predator–prey model with threshold harvesting

Dynamics of a Predator‐Prey Population in the Presence of Resource Subsidy under the Influence of Nonlinear Prey Refuge and Fear Effect

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