Global dynamics of stochastic predator–prey model with mutual interference and prey defense

Upadhyay, Ranjit Kumar; Parshad, Rana D.; Antwi-Fordjour, Kwadwo; Quansah, Emmanuel; Kumari, Shipra

doi:10.1007/s12190-018-1207-7

Cited by 16 publications

(5 citation statements)

References 24 publications

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“…affect our ecological system and hence are not ignorable to get more realistic results. Thus, to asses the impact of environmental fluctuations, we convert deterministic model system (1) into stochastic by introducing environmental noise term into each equation [2,9,11,14,15,31].…”

Section: Model Formulationmentioning

confidence: 99%

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Modeling the influence of human population and human population augmented pollution on rainfall

Misra¹,

Agrawal²,

Lata³

2022

DCDS-B

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Worldwide, human population is increasing continuously and this has magnified the level of pollutants in the environment. Pollutants affect the human population as well as the environmental ecology including rainfall. Here, we formulate a mathematical model comprising ordinary differential equations to see the effect of human population and pollution caused by human population on the dynamics of rainfall. In the modeling process, it is assumed that the augmentation in the density of human population increases the concentration of pollutants; however, decreases the rate of formation of cloud droplets. It is also assumed that pollutants have negative impact on human population and affect the precipitation. The feasibility of all equilibrium and their stability properties are discussed. Further, to capture the effect of environmental randomness, the proposed model is also analyzed by incorporating white noise terms. For the proposed stochastic model, we have established the existence and uniqueness of global positive solution. It is also shown that system possesses a unique stationary distribution with some restrictions. The model analysis reveals that rainfall may decrease or increase due to the anthropogenic emission of pollutants in the atmospheric environment. Finally, for the validation of analytical findings, numerical simulations are presented.

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Section: Model Formulationmentioning

confidence: 99%

“…Consider Ω ϱ = {ω : τ ϱ ≤ T } ∀ ϱ ≥ ϱ 1 , then by (31), P(Ω ϱ ) ≥ ϵ. Thus ∀ ω ∈ Ω ϱ , there is at least one of N (τ ϱ , ω), C d (τ ϱ , ω), C r (τ ϱ , ω), P (τ ϱ , ω) equals either ϱ or 1 ϱ .…”

Section: Appendix B Proof Of Theorem 42mentioning

confidence: 99%

Modeling the influence of human population and human population augmented pollution on rainfall

Misra¹,

Agrawal²,

Lata³

2022

DCDS-B

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“…Assume that 0 < m 2 ≤ 1, as per literature on mutual interference [1,2]. In this paper, we consider the general logistic growth and the generalized Holling type functional response, see [3,4]:…”

Section: Model Formulationmentioning

confidence: 99%

Dynamics of a predator-prey model with generalized Holling type functional response and mutual interference

Antwi-Fordjour,

Parshad,

Beauregard

2020

Preprint

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Mutual interference and prey refuge are important drivers of predatorprey dynamics. The "exponent" or degree of mutual interference has been under much debate in theoretical ecology. In the present work, we investigate the interplay of the mutual interference exponent, on the behavior of a predatorprey model with a generalized Holling type functional response. We investigate stability properties of the system and derive conditions for the occurrence of saddle-node and Hopf-bifurcations. A sufficient condition for extinction of the prey species has also been derived for the model. In addition, we investigate the effect of a prey refuge on the population dynamics of the model and derive conditions for the prey refuge that would yield persistence of populations. We provide additional verification our analytical results via numerical simulations. Our findings are in accordance with classical experimental results in ecology [23], that show that extinction of predator and prey populations is possible in a finite time period -but that bringing in refuge can effectively cause persistence.

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“…In this study, they determined that extinction due to group defence combined with enrichment can be prevented by introducing mutual interference of predators. For further discussions of mutual interference with other types of functional response, see [15,4,54,55,56,19].…”

Section: Introductionmentioning

confidence: 99%

Fear-driven extinction and (de)stabilization in a predator-prey model incorporating prey herd behavior and mutual interference

Antwi-Fordjour¹,

Parshad²,

Thompson³

et al. 2021

Preprint

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A deterministic two-species predator-prey model with prey herd behavior is considered incorporating mutual interference and the effect of fear. We provide guidelines to the dynamical analysis of biologically feasible equilibrium points. We give conditions for the existence of some local and global bifurcations at the coexistence equilibrium. We also show that fear can induce extinction of the prey population from a coexistence zone in finite time. Our numerical simulations reveal that varying the strength of fear of predators with suitable choice of parameters can stabilize and destabilize the coexistence equilibrium solutions of the model. Additionally, we discuss the outcome of introducing a constant harvesting effort to the predator population in terms of changing the dynamics of the system, in particular, from finite time extinction to stable coexistence. Furthermore, we perform extensive numerical experiments to visualize the dynamical behavior of the model and substantiate the results we obtained.

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Global dynamics of stochastic predator–prey model with mutual interference and prey defense

Cited by 16 publications

References 24 publications

Modeling the influence of human population and human population augmented pollution on rainfall

Modeling the influence of human population and human population augmented pollution on rainfall

Dynamics of a predator-prey model with generalized Holling type functional response and mutual interference

Fear-driven extinction and (de)stabilization in a predator-prey model incorporating prey herd behavior and mutual interference

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