Global dynamics and bifurcation in a stage structured prey–predator fishery model with harvesting

Chakraborty, Kunal; Jana, Soovoojeet; Kar, Tapan Kumar

doi:10.1016/j.amc.2012.03.005

Cited by 98 publications

(46 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Proof It follows from (2.25) that, indeed, for enough small ε > 0, namely, for 27) we have the inequality…”

Section: Theorem 24 Letmentioning

confidence: 99%

“…During the last decades, many scholars investigated the influence of the harvesting to predator-prey or competition system; see [22][23][24][25][26][27] and the references therein. Chakraborty, Das, and Kar [24] argued that it is necessary to harvest the population but harvesting should be regulated, so that both the ecological sustainability and conservation of the species can be implemented in a long run.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Permanence, partial survival, extinction, and global attractivity of a nonautonomous harvesting Lotka–Volterra commensalism model incorporating partial closure for the populations

Liu

Xie

2018

Adv Differ Equ

View full text Add to dashboard Cite

We propose and study a nonautonomous harvesting Lotka-Volterra commensalism model incorporating partial closure for the populations. By using the differential inequality theory we obtain sufficient conditions that ensure the extinction, partial survival, and permanence of the system. By applying the fluctuation lemma we establish sufficient conditions that ensure the extinction of one of the components and the stability of the the other one. For the permanent case, by constructing a suitable Lyapunov function we obtain some sufficient conditions for the globally attractivity of the positive solution of the system. Examples, together with their numeric simulations, show the feasibility of the main results. To ensure the stable coexistence of the two species, the harvesting area should be carefully restricted.

show abstract

“…Proof It follows from (2.25) that, indeed, for enough small ε > 0, namely, for 27) we have the inequality…”

Section: Theorem 24 Letmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Permanence, partial survival, extinction, and global attractivity of a nonautonomous harvesting Lotka–Volterra commensalism model incorporating partial closure for the populations

Liu

Xie

2018

Adv Differ Equ

View full text Add to dashboard Cite

show abstract

“…Our goal is to maximize the present value J subject to the equation (3) by following the Pontryagin's maximum principle [19] into equations (7) and (9) 1 2 3 1 3 3 1 5 2 3 3 1 5 1 3 2 1 2 1 1 3 1 1 1 3 2 2 1 1 1 3 1 1 1 3 1 3 1 1 2 1 3 3 1 5 2 1 3 2 1 3 2 2 3 1 2 3 1 5 3 1 5 2 1 3 1 3 2 1 3 1 1 3 1 1 1 3 2 1 3 1 2 3 1 1 1 3 1 5 3 1 1 2 1 3 1 1 1 (10) . 3 1 1 3 1 3 3 1 3 5 3 1 3 1 1 3 1 5 1 3 3 1 3 3 3 3 3 3 3 …”

Section: Optimal Harvesting Policy Of the Populationmentioning

confidence: 99%

“…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

View full text Add to dashboard Cite

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.

show abstract

“…For detailed calculations one can see Chakraborty et al [34], Li and Muldowney [35], Bunomo et al [36], Martin [37] etc.…”

Section: Global Stabilitymentioning

confidence: 99%

An ecological perspective on marine reserves in prey–predator dynamics

Chakraborty

Das²,

Kar

2013

J Biol Phys

Self Cite

View full text Add to dashboard Cite

This paper describes a prey-predator type fishery model with prey dispersal in a two-patch environment, one of which is a free fishing zone and other is a protected zone. The existence of possible steady states, along with their local stability, is discussed. A geometric approach is used to derive the sufficient conditions for global stability of the system at the positive equilibrium. Relative size of the reserve is considered as control in order to study optimal sustainable yield policy. Subsequently, the optimal system is derived and then solved numerically using an iterative method with Runge-Kutta fourth-order scheme. Numerical simulations are carried out to illustrate the importance of marine reserve in fisheries management. It is noted that the marine protected area enables us to protect and restore multi-species ecosystem. The results illustrate that dynamics of the system is extremely interesting if simultaneous effects of a regulatory mechanism like marine reserve is coupled with harvesting effort. It is observed that the migration of the resource, from protected area to unprotected area and vice versa, is playing an important role towards the standing stock assessment in both the areas which ultimately control the harvesting efficiency and enhance the fishing stock up to some extent.

show abstract

Global dynamics and bifurcation in a stage structured prey–predator fishery model with harvesting

Cited by 98 publications

References 34 publications

Permanence, partial survival, extinction, and global attractivity of a nonautonomous harvesting Lotka–Volterra commensalism model incorporating partial closure for the populations

Permanence, partial survival, extinction, and global attractivity of a nonautonomous harvesting Lotka–Volterra commensalism model incorporating partial closure for the populations

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

An ecological perspective on marine reserves in prey–predator dynamics

Contact Info

Product

Resources

About