Persistence and Extinction of One-Prey and Two-Predators System

Dubey, B.; Upadhyay, Ranjit Kumar

doi:10.15388/na.2004.9.4.15147

Cited by 72 publications

(35 citation statements)

References 27 publications

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“…In this, the predators compete with one another when prey are scarce. Dubey and Upadhyay (2004) propose another model for one prey and two predator interactions and discuss the factors resulting in either persistence or extinction. Alebraheem's (2012) model indicates that coexistence of two predators (y and z) depends on the efficiencies of the predators' conversion of prey biomass into predator offspring being similar.…”

Section: One-prey -Two-predator Systemmentioning

confidence: 99%

Ecological perspective of the diversity of functional responses

Pervez

Singh²,

Bozdoğan

2018

European Journal of Environmental Sciences

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Prey-predator interactions have been modelled by numerous workers. Ecologists have continuously modified Lotka-Volterra equations in order to provide more realistic descriptions of the complexity of these interactions. The response of predator(s) to increasing prey density can be best described in terms of a functional response, which is an important criterion determining the success or failure of predator(s) to control fluctuating prey populations. The functional response of a predator is further differentiated into Holling's Type I, II, III, IV and V. We discuss one-prey and one-predator interactions, in which the models are modified by the inclusion of steady-state satiation and growth factors. We review situations where two prey and one predator interact, and vice versa. We also discuss Holling's Type IV model relevant to competition and food chains. There is a need to examine functional responses as these models were mostly developed by pure mathematicians and their relevance to field conditions remains largely untested. Prey-predator interactions can be affected even by small factors and ecologists should include these models in their experimental design when attempting to predict realistic interactions.

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Section: One-prey -Two-predator Systemmentioning

confidence: 99%

Ecological perspective of the diversity of functional responses

Pervez

Singh²,

Bozdoğan

2018

European Journal of Environmental Sciences

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“…We present effects the strength of seasonality ( ) on persistence and extinction of predators in prey predator systems, which is discussed through investigating smooth function (1) in the model (3) as it is explained in the system (4). Different values of epsilon are assumed, the other parameters and initial conditions are fixed in the numerical simulations as follows: This can be interpreted mathematically as follows:…”

Section: The Strength Of Seasonality (Epsilon)mentioning

confidence: 99%

“…Non linear differential equations are effective tool to describe these systems. The dynamical behaviors of species interactions involve the persistence and extinction of species, which have been taken into consideration by some researchers [3,4].…”

Section: Introductionmentioning

confidence: 99%

Effects the strength of seasonality on persistence and extinction in prey predator models

Alebraheem¹,

Hasan²

2014

AIP Conference Proceedings

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A model of two competing predators sharing one prey is introduced. In the model, the seasonality in the functional response is investigated. Kolmogorov's conditions are obtained to validate the values of the parameters. In the numerical simulations, we show the effects of the seasonality strength on the persistence and extinction of predators, the results are supported through the mathematical analysis.

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“…This completes the proof of the lemma. , Then a sufficient conditions [18] for ̇ to be negative definite is that…”

Section: Boundedness Of the Systemmentioning

confidence: 99%

Effect of Exotic Species on a System of Native Prey-Predator Populations : A Model

Misra¹,

Kushwah²,

Sikarwar³

2013

AJCAM

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In this paper, a mathemat ical model is proposed to study the effect of exotic predator population on a system of native prey-predator population. The model includes three state variables viz., density of native prey, density of native predator and density of exotic predator. The stability analysis of all the feasible equilibria are carried out and also the possibility of Hopf-bifu rcation of the interior equilibriu m point is investigated for the parameter 2 ; the predation rate of exotic predator. By vary ing the parameter 2 , a change in stability behaviour of the interior equilibriu m is also observed. The stability and direction of bifurcating periodic solution is discussed. Finally the analytical results are supported by numerical simulat ion.

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Persistence and Extinction of One-Prey and Two-Predators System

Cited by 72 publications

References 27 publications

Ecological perspective of the diversity of functional responses

Ecological perspective of the diversity of functional responses

Effects the strength of seasonality on persistence and extinction in prey predator models

Effect of Exotic Species on a System of Native Prey-Predator Populations : A Model

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