2014
DOI: 10.1155/2014/429086
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Abstract: In the present paper, I study a prey-predator model with multiple time delays where the predator population is regarded as generalist. For this regard, I consider a Holling-Tanner prey-predator system where a constant time delay is incorporated in the logistic growth of the prey to represent a delayed density dependent feedback mechanism and the second time delay is considered to account for the length of the gestation period of the predator. Predator’s interference in predator-prey relationship provides bette… Show more

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Cited by 13 publications
(11 citation statements)
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“…f (x) is the specific growth rate of prey in the absence of predator and g(x) is the predator response function. It is shown that the most commonly used Holling Type II functional response, given by g(x(t)) = αx 1+αhx , can be modified to g(x(t)) = α(1−m)x 1+α(1−m)hx [18,19,20,21] in the presence of prey refuge. Here α is the prey attack coefficient, h is the handling time and m (0 < m < 1) is the degree or strength of prey refuge.…”
Section: Introductionmentioning
confidence: 99%
“…f (x) is the specific growth rate of prey in the absence of predator and g(x) is the predator response function. It is shown that the most commonly used Holling Type II functional response, given by g(x(t)) = αx 1+αhx , can be modified to g(x(t)) = α(1−m)x 1+α(1−m)hx [18,19,20,21] in the presence of prey refuge. Here α is the prey attack coefficient, h is the handling time and m (0 < m < 1) is the degree or strength of prey refuge.…”
Section: Introductionmentioning
confidence: 99%
“…In food chain models, different consumers show different gestation time, so it is very important and significant observation to study impact of multiple time lags as gestation delays of different consumers in one food chain model. Jana (2014) studies the stabilizing effect of prey refuge and predator's interference on the dynamics of prey with delayed growth and generalist predator with delayed gestation. Jana and Samanta (2014) show the complex dynamical results of a multi-delayed ratio-dependent prey-predator system with prey harvesting under stochastic environment.…”
Section: Introductionmentioning
confidence: 99%
“…On a fairly realistic ecological model with generalist top predator, Upadhyay et al (2007) investigate the influence of environmental noise and show the importance of the noise amplitude on the trophic level and the susceptibility of populations to environmental noise. Complex dynamical behavior of a biological system arises as a consequence of time delay (with significant time delay) which may exhibit limit cycle oscillations (Ruan 2009) and chaos (Mackey and Glass 1977;Jana 2014;Jana et al 2014). In reality, time delays occur in almost every ecological situation and assume to be one of the most prominent reason of regular fluctuations on population biomass (Jana 2014;Jana et al 2014Jana et al , 2015.…”
Section: Introductionmentioning
confidence: 99%
“…Complex dynamical behavior of a biological system arises as a consequence of time delay (with significant time delay) which may exhibit limit cycle oscillations (Ruan 2009) and chaos (Mackey and Glass 1977;Jana 2014;Jana et al 2014). In reality, time delays occur in almost every ecological situation and assume to be one of the most prominent reason of regular fluctuations on population biomass (Jana 2014;Jana et al 2014Jana et al , 2015. Ruan (2009) presents a brief review on prey-predator models with descrete delay for both Kolmogorov and non-Kolmogorov type model system.…”
Section: Introductionmentioning
confidence: 99%
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