Modelling and analysis of prey-predator model involving predation of mature prey using delay differential equations

Kumar, Pankaj; Raj, Shiv

doi:10.3934/naco.2021035

Cited by 3 publications

(2 citation statements)

References 19 publications

(26 reference statements)

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“…Few studies have investigated the effect of prey maturation on a predator-prey model through mathematical modelling. Predation of mature prey can be evaluated using delay differential equations (Kumar et al, 2021). Time lag is a crucial factor that should be included in the mathematical model to examine the dynamic behaviour of these types of biological systems (Kumar et al, 2022).…”

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confidence: 99%

Modelling the Multiteam Prey–predator Dynamics Using the Delay Differential Equation

Raj

Kumar

2023

MJS

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In nature, many species form teams and move in herds from one place to another. This helps them in reducing the risk of predation. Time delay caused by the age structure, maturation period, and feeding time is a major factor in real-time prey–predator dynamics that result in periodic solutions and the bifurcation phenomenon. This study analysed the behaviour of teamed-up prey populations against predation by using a mathematical model. The following variables were considered: the prey population Pr1, the prey population Pr2, and the predator population Pr3. The interior equilibrium point was calculated. A local satiability analysis was performed to ensure a feasible interior equilibrium. The effect of the delay parameter on the dynamics was examined. A Hopf bifurcation was noted when the delay parameter crossed the critical value. Direction analysis was performed using the centre manifold theorem. The graphs of analytical results were plotted using MATLAB.

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Section: Introductionmentioning

confidence: 99%

Modelling the Multiteam Prey–predator Dynamics Using the Delay Differential Equation

Raj

Kumar

2023

MJS

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“…The unique positive equilibrium point (equilibrium at the interior of the first quadrant) is globally asymptotically stable [22,28]. In this work, we introduce two modifications to the prey growth function in the Leslie-Gower model considering i) the prey is affected by the Allee effect phenomenon, and ii) a time lag appearing in the intraspecific interaction of prey, representing a delayed prey growth effect [13,20]. Any mechanism leading to a positive relationship between a component of individual fitness and the number or density of conspecifics can be named as a Allee effect [26,27]; it describes a scenario in which populations at low population sizes, are affected by a positive relationship between population growth rate and density, increasing their likelihood of extinction [6,7]; it has been denominated in different ways in Population Dynamics [15] and depensation in Fisheries Sciences [5,15].…”

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Stability of a Leslie-Gower type predator-prey model with a strong Allee effect with delay

Cruz

2022

Sel.mat

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In this paper, a modified Leslie-Gower type predator-prey model introducing in prey population growth a delayed strong Allee effect is studied. The Leslie-Gower model with Allee effect has none, one or two positive equilibrium points but the incorporation of a time delay in the growth rate destabilizes the system, breaking the stability when the delay cross a critical point. The existence of a Hopf bifurcation is studied in detail and the numerical simulations confirm the theoretical results showing the different scenarios. We present biological interpretations for species prey-predator type.

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Predator and n-classes-of-prey model incorporating extended Holling type Ⅱ functional response for n different prey species

Fatah¹,

Mustafa²,

Amin

2022

MATH

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<abstract><p>In this paper, the Holling type Ⅱ functional response extended for n different species of prey and the dynamics of interactions between one predator species and its n different classes of prey are modeled. Positivity, boundedness and permanence of all solutions of the model are proved. An ecological threshold parameter for the predator free equilibrium point of the model is established. Local stability and global stability of the predator free equilibrium point are discussed. Furthermore, we also studied that the reproduction number <italic>R</italic><sub>0</sub> determines whether the equilibrium points are asymptotically stable or unstable. In addition, the model was solved numerically to confirm the analytical results.</p></abstract>

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Modelling and analysis of prey-predator model involving predation of mature prey using delay differential equations

Cited by 3 publications

References 19 publications

Modelling the Multiteam Prey–predator Dynamics Using the Delay Differential Equation

Modelling the Multiteam Prey–predator Dynamics Using the Delay Differential Equation

Stability of a Leslie-Gower type predator-prey model with a strong Allee effect with delay

Predator and n-classes-of-prey model incorporating extended Holling type Ⅱ functional response for n different prey species

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