The role of top predator interference on the dynamics of a food chain model

Upadhyay, Ranjit Kumar; Naji, Raid Kamel; Raw, S. N.; Dubey, B.

doi:10.1016/j.cnsns.2012.08.020

Cited by 28 publications

(26 citation statements)

References 27 publications

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“…• We show the three species model proposed in [57], and its spatially explicit version, can blow-up in finite time, for sufficiently large initial data via theorem 3.2 and corollary 1.…”

Section: 2mentioning

confidence: 99%

“…We impose different assumptions from the ones assumed in [57] to formulate the spatially explicit form of the differential equations which describe the model. The detailed meaning of the different parameters is given in [57].…”

Section: Model Formulationmentioning

confidence: 99%

“…• The spatially explicit form of the three species model proposed in [57], possesses spatio-temporal chaos. Also time delays in the temporal model, affect both the blow-up dynamics as well as the chaotic dynamics.…”

Section: 2mentioning

confidence: 99%

“…The goal is that r will hunt and depredate on v, its favorite food, thus lowering the population of v. The dynamical interaction between v and u is modeled via standard Rosenzweig-McArthur scheme [23], while the dynamics between r and v is modeled via a Leslie-Gower formulation, where interference in the top predator r is assumed, and this is modeled via a Beddington DeAngelis functional response [47]. Upadhyay et al [57] have proposed a tri-trophic hybrid food chain model to study such a system. Here the prey population density u serves as the only food for the intermediate specialist predator population of density v. This population v serves as a favorite food for the generalist top predator population of density r.…”

Section: Model Formulationmentioning

confidence: 99%

“…• Can interference cause a population explosion in certain generalist predator biological agent populations? To answer these we investigate the three species model proposed in [57], where the interaction between the intermediate predator and the top predator is modeled according to the Beddington-DeAngelis type functional response. This response models predator interference in the top predator r [46,47].…”

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confidence: 99%

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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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“…• We show the three species model proposed in [57], and its spatially explicit version, can blow-up in finite time, for sufficiently large initial data via theorem 3.2 and corollary 1.…”

Section: 2mentioning

confidence: 99%

Section: Model Formulationmentioning

confidence: 99%

Section: 2mentioning

confidence: 99%

Section: Model Formulationmentioning

confidence: 99%

mentioning

confidence: 99%

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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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Complex dynamics induced by multiple gestation delays in a Leslie–Gower‐type system with competitive interference

Ojha

Thakur

2023

Math Methods in App Sciences

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The dynamics of food consumption by higher trophic level is complicated as its availability, choice, and consequently their development. The top predator interference has a strong influence on the dynamic structure of the tritrophic food chain system. The proposed article deals with the characteristic features of a three‐tire modified Leslie–Gower model with a one‐prey two‐predator system with the assumption of multiple gestation delays. The intermediate predator of the food chain is taken as a specialist type, whereas the growth of top predator is assumed by sexual reproduction. Two different response functions named Monod–Haldane (M‐H) and Beddington–DeAngelis (B‐D) are considered for the modeling of system dynamics. The population densities of intermediate and top predators are assumed to be affected by two different gestation delays. The boundedness and positive equilibria and their stability conditions are examined theoretically for the delay‐free system. The local and global stability conditions of the delayed system are also determined. With the help of normal form theory and central manifold arguments, the properties of bifurcating periodic solutions are carried out. The numerical computation is performed to validate our analytical findings that show the different dynamical outcomes such as periodic and chaotic dynamics. The Hopf‐bifurcation scenario for different parameters of the model system is well studied. Further, the stability behavior of multiple delays for the different cases is investigated. The system shows chaotic behavior when the gestation delay of intermediate predators is large enough. It is also observed that the top predator density is highly fluctuating through the creation of chaos by the inclusion of time delay. Finally, the time delay destabilizing effect is noticed for three‐way interactions among prey, intermediate predator, and top predator, highlighting its significance in chaotic dynamics.

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An Exploration of the Effects of Periodic Top Predator Interference and Hunting on a Predator-Prey System

Acotto,

Bardi,

Manzini

et al. 2024

Trends in Biomathematics: Exploring Epidemics, Eco-Epidemiological Systems, and Optimal Control Strategies

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The role of top predator interference on the dynamics of a food chain model

Cited by 28 publications

References 27 publications

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

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

Complex dynamics induced by multiple gestation delays in a Leslie–Gower‐type system with competitive interference

An Exploration of the Effects of Periodic Top Predator Interference and Hunting on a Predator-Prey System

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