Modeling the effect of mutual interference in a delay-induced predator-prey system

Upadhyay, Ranjit Kumar; Agrawal, Rashmi

doi:10.1007/s12190-014-0822-1

Cited by 9 publications

(5 citation statements)

References 22 publications

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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%

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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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Section: Model Formulationmentioning

confidence: 99%

“…of model(3), we obtain the following two interior equilibrium points E1 2 (3.12437, 30.6886) and E 2 2 (6.67563, 31.7032) and the predator-free equilibrium point is E 1 (10, 0). The eigenvalues associated with E 1 2 (3.12437, 30.6886) are −0.343043 and 0.170265, hence E 1 2 is a saddle.…”

mentioning

confidence: 92%

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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“…the effect of delay on both two and three species predator-prey models. Upadhyay and Agrawal [55] investigated the effect of mutual interference on the dynamics of delay induced predator prey system, and determined the conditions under which the model becomes globally asymptotically stable around the nonzero equilibria. Recently, Jana et al [56] have made an attempt to understand the role of top predator interference and gestation delay on the dynamics of a three species food chain model.…”

Section: Effect Of Time Delaymentioning

confidence: 99%

Predator interference effects on biological control: The “paradox” of the generalist predator revisited

Parshad

Bhowmick

Quansah

et al. 2016

Communications in Nonlinear Science and Numerical Simulation

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Abstract. An interesting conundrum in biological control questions the efficiency of generalist predators as biological control agents. Theory suggests, generalist predators are poor agents for biological control, primarily due to mutual interference. However field evidence shows they are actually quite effective in regulating pest densities. In this work we provide a plausible answer to this paradox. We analyze a three species model, where a generalist top predator is introduced into an ecosystem as a biological control, to check the population of a middle predator, that in turn is depredating on a prey species. We show that the inclusion of predator interference alone, can cause the solution of the top predator equation to blow-up in finite time, while there is global existence in the no interference case. This result shows that interference could actually cause a population explosion of the top predator, enabling it to control the target species, thus corroborating recent field evidence. Our results might also partially explain the population explosion of certain species, introduced originally for biological control purposes, such as the cane toad (Bufo marinus) in Australia, which now functions as a generalist top predator. We also show both Turing instability and spatio-temporal chaos in the model. Lastly we investigate time delay effects.

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“…This delay can be the delay of gestation period, 17 delay of maturation, 18 delay of immune system to respond, 19 and so forth. In biological and ecological modeling, many authors have studied the effect of a time delay in many mathematical models and shown the existence of Hopf bifurcation which is an important characteristic of a delay differential equation 20‐22 …”

Section: Introductionmentioning

confidence: 99%

“…In biological and ecological modeling, many authors have studied the effect of a time delay in many mathematical models and shown the existence of Hopf bifurcation which is an important characteristic of a delay differential equation. [20][21][22] The theory of fractional calculus, a generalization of integral order differentiation and integration, has been developed fruitfully in the past few years. Fractional-order differential equations (FODEs) are related to systems with memory which exists in most biological systems and consequently it is claimed that FODEs are, at least, as stable as their integer-order counterpart.…”

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confidence: 99%

Stability analysis of a fractional‐order delay dynamical model on oncolytic virotherapy

Singh

Pandey

2020

Math Methods in App Sciences

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In this manuscript, the main objective is to introduce the derivatives of fractional-order into a delayed dynamical model of oncolytic virotherapy. The system consists of populations of infected cells, uninfected cells, and virus particles. The local asymptotic stability of all the equilibrium points is discussed by analyzing the corresponding characteristic polynomials. The existence of Hopf bifurcation is shown due to the effect of delay. The fractional-order dynamical system is compared with the integer order counterpart. Numerical simulations are also carried out to verify how the fractional-order model is more stable than its integer-order counterpart and fractional-order parameter can be used to pacify the effect of delay.

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Modeling the effect of mutual interference in a delay-induced predator-prey system

Cited by 9 publications

References 22 publications

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

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

Predator interference effects on biological control: The “paradox” of the generalist predator revisited

Stability analysis of a fractional‐order delay dynamical model on oncolytic virotherapy

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