Dynamical properties of a prey-predator-scavenger model with quadratic harvesting

Gupta, R. N.; Chandra, Peeyush

doi:10.1016/j.cnsns.2017.01.026

Cited by 31 publications

(22 citation statements)

References 24 publications

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“…Clearly, λ 1 = -d 11 , λ 2 = -d 21 , which are always negative. Hence, the stability of the boundary equilibrium E 2 is determined by the following equations:…”

Section: The Local Stability Of the Boundary Equilibrium Ementioning

confidence: 99%

“…Conversion rate of nutrients into the reproduction of the mature top predator d 11 Death rate of the immature predator d 12 Death rate of the mature predator d 21 Death rate of the immature top predator d 22 Death rate of the mature top predator…”

Section: Introductionmentioning

confidence: 99%

“…The 'prey-predator-top-predator' system (the top predator consumes only the predator trophic level), as one of the most important food-chain models [16][17][18][19][20][21], takes the form…”

Section: Introductionmentioning

confidence: 99%

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Dynamical behaviors of a food-chain model with stage structure and time delays

et al. 2018

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Incorporating two delays (τ 1 represents the maturity of predator, τ 2 represents the maturity of top predator), we establish a novel delayed three-species food-chain model with stage structure in this paper. By analyzing the characteristic equations, constructing a suitable Lyapunov functional, using Lyapunov-LaSalle's principle, the comparison theorem and iterative technique, we investigate the existence of nonnegative equilibria and their stability. Some interesting findings show that the delays have great impacts on dynamical behaviors for the system: on one hand, if τ 1 ∈ (m 1 , m 2 ) and τ 2 ∈ (m 4 , +∞), then the boundary equilibrium E 2 (x 0 , y 0 1 , y 0 2 , 0, 0) is asymptotically stable (AS), i.e., the prey species and the predator species will coexist, the top-predator species will go extinct; on the other hand, if τ 1 ∈ (m 2 , +∞), then the axial equilibrium E 1 (k, 0, 0, 0, 0) is AS, i.e., all predators will go extinct. Numerical simulations are great well agreement with the theoretical results.

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“…Clearly, λ 1 = -d 11 , λ 2 = -d 21 , which are always negative. Hence, the stability of the boundary equilibrium E 2 is determined by the following equations:…”

Section: The Local Stability Of the Boundary Equilibrium Ementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dynamical behaviors of a food-chain model with stage structure and time delays

et al. 2018

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“…In [7], the authors have made a mathematical study of a bioeconomic model of fishing for multisite, exploited by several fishermen, except one of them which is defined as not exploitable free fishing zone. In [8], the authors proposed and analyzed an extended model for the prey-predator-scavenger in presence of harvesting to study the effects of harvesting of predator as well as scavenger.…”

Section: Introductionmentioning

confidence: 99%

“…In recent years, the biodiversity of marine populations is threatened by human impact, more precisely, by harvesting, which required many scientists to study bioeconomic models of fishery [7,8]. In [7], the authors have made a mathematical study of a bioeconomic model of fishing for multisite, exploited by several fishermen, except one of them which is defined as not exploitable free fishing zone.…”

Section: Introductionmentioning

confidence: 99%

The Impact of Price on the Profits of Fishermen Exploiting Tritrophic Prey-Predator Fish Populations

Bentounsi

Agmour

Achtaich

et al. 2018

International Journal of Differential Equations

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We define and study a tritrophic bioeconomic model of Lotka-Volterra with a prey, middle predator, and top predator populations. These fish populations are exploited by two fishermen. We study the existence and the stability of the equilibrium points by using eigenvalues analysis and Routh-Hurwitz criterion. We determine the equilibrium point that maximizes the profit of each fisherman by solving the Nash equilibrium problem. Finally, following some numerical simulations, we observe that if the price varies, then the profit behavior of each fisherman will be changed; also, we conclude that the price change mechanism improves the fishing effort of the fishermen.

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