Optimal control of harvest and bifurcation of a prey–predator model with stage structure

Chakraborty, Kunal; Chakraborty, Milon; Kar, Tapan Kumar

doi:10.1016/j.amc.2011.03.139

Cited by 50 publications

(30 citation statements)

References 15 publications

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“…The rate of increase of the predator population depends on the amount of prey biomass it converts as food. Thus according to Hollying type II functional response [15] the two populations are modeled as follows: where x is the prey density at time t, y is the predator density at time t, r is the intrinsic prey growth rate, k is the prey carrying capacity, w is the maximum per capita predation rate, 1 w is the predator biomass to the prey (conversion rate), p is the wildebeest poaching rate in Serengeti, c is lion death rate due to retaliatory killing, f is the percentage of wildebeest resilient to drought, hence ( ) 1 f − is the wildebeest death rate due to drought, e is the percentage of lion resilient to drought, hence ( ) 1 e − is the lion death rate due to drought, a is the predator half saturation and 2 a is the lion mortality rate.…”

Section: The Model With Threatsmentioning

confidence: 99%

“…The application of anti-poaching patrols 1 u is used to optimize the objective function J while we set the con-struction of strong boma 2 u and construction of dams 3 u to zero. In Figure 1, the results show a significant difference in the prey population with optimal strategy compared to prey population without control while no effect to predator population as the control is taken only to prey species.…”

Section: Strategy A: Application Of Anti-poaching Patrols For Controlmentioning

confidence: 99%

“…It is clear that predator population depends on their prey species for survival and affects the survival and fecundity rate of prey species. Therefore, predator population is affected by changes in prey population in a complex and cyclic predator-prey relationship [1].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Optimal Control of a Threatened Wildebeest-Lion Prey-Predator System in the Serengeti Ecosystem

Sagamiko¹,

Shaban²,

Nahonyo³

et al. 2015

OJE

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We develop a two-species prey-predator model in which prey is wildebeest and predator is lion. The threats to wildebeest are poaching and drought while to lion are retaliatory killing and drought. The system is found in the Serengeti ecosystem. Optimal control theory is applied to investigate optimal strategies for controlling the threats in the system where anti-poaching patrols are used for poaching, construction of strong bomas for retaliatory killing and construction of dams for drought control. The possible impact of using a combination of the three controls either one at a time or two at a time on the threats facing the system is also examined. We observe that the best result is achieved by using all controls at the same time, where a combined approach in tackling threats to yield optimal results is a good approach in the management of wildlife populations.

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Section: The Model With Threatsmentioning

confidence: 99%

Section: Strategy A: Application Of Anti-poaching Patrols For Controlmentioning

confidence: 99%

See 1 more Smart Citation

Optimal Control of a Threatened Wildebeest-Lion Prey-Predator System in the Serengeti Ecosystem

Sagamiko¹,

Shaban²,

Nahonyo³

et al. 2015

OJE

View full text Add to dashboard Cite

show abstract

“…Some authors considered harvesting for the prey population only (for examples in [1,3,4,5]), harvesting for the predator population only (for examples in [ 6,7,8,9,10,11,12]), and harvesting for both predator and prey populations (for examples in [13,14]). Most of predator-prey model with harvesting was related to the economic problems including maximum profit problem, taxation effect, and total discounted net revenue problem, for examples in [1,14,15].…”

Section: Introductionmentioning

confidence: 99%

Optimal harvesting policy of predator-prey model with free fishing and reserve zones

Toaha

Rustam

2017

AIP Conference Proceedings

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Abstract. The present paper deals with an optimal harvesting of predator-prey model in an ecosystem that consists of two zones, namely the free fishing and prohibited zones. The dynamics of prey population in the ecosystem can migrate from the free fishing to the prohibited zone and vice versa. The predator and prey populations in the free fishing zone are then harvested with constant efforts. The existence of the interior equilibrium point is analyzed and its stability is determined using Routh-Hurwitz stability test. The stable interior equilibrium point is then related to the problem of maximum profit and the problem of present value of net revenue. We follow the Pontryagin's maximal principle to get the optimal harvesting policy of the present value of the net revenue. From the analysis, we found a critical point of the efforts that makes maximum profit. There also exists certain conditions of the efforts that makes the present value of net revenue becomes maximal. In addition, the interior equilibrium point is locally asymptotically stable which means that the optimal harvesting is reached and the unharvested prey, harvested prey, and harvested predator populations remain sustainable. Numerical examples are given to verify the analytical results.

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“…Two species continuous time models of predator (natural enemy)-prey (pest) type of interaction with functional response of the predator to its prey have been extensively discussed in the literature [2][3][4][5][6]. Andrews [1] Many authors researched Holling type IV population models [8].…”

Section: Introductionmentioning

confidence: 99%

Harvesting and Hopf Bifurcation in a Prey-Predator Model with Holling Type IV Functional Response

Agarwal¹,

Pathak²

2012

International Journal of Mathematics and Soft Computing

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Abstract.This paper aims to study the effect of Harvesting on predator species with time-delay on a Holling type-IV prey-predator model. Harvesting has a strong impact on the dynamic evolution of a population. Two delays are considered in the model of this paper to describe the time that juveniles of prey and predator take to mature. Dynamics of the system is studied in terms of local and Hopf bifurcation analysis. Finally, numerical simulation is done to support the analytical findings.

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Optimal control of harvest and bifurcation of a prey–predator model with stage structure

Cited by 50 publications

References 15 publications

Optimal Control of a Threatened Wildebeest-Lion Prey-Predator System in the Serengeti Ecosystem

Optimal Control of a Threatened Wildebeest-Lion Prey-Predator System in the Serengeti Ecosystem

Optimal harvesting policy of predator-prey model with free fishing and reserve zones

Harvesting and Hopf Bifurcation in a Prey-Predator Model with Holling Type IV Functional Response

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