Stability analysis and optimal impulsive harvesting for a delayed stage-structured self dependent two compartment commercial fishery model

Sharma, Amit; Gupta, B. D.; Dhar, Joydip; Srivastava, S. K.; Sharma, Payal

doi:10.1007/s40435-021-00866-5

Cited by 6 publications

(3 citation statements)

References 20 publications

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“…• predator-prey systems where either one of the species or both are subject to harvesting, structured and Lotka-Volterra models which -without delay in impulsive harvesting or an impulsive system with continuous harvesting -are well-studied areas, see, for example, [9,34,35,36,37,38,39,40,41,42];…”

Section: Numerical Simulations and Discussionmentioning

confidence: 99%

Optimality and sustainability of delayed impulsive harvesting

Lawson,

Braverman

2022

Preprint

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We consider a logistic differential equation subject to impulsive delayed harvesting, where the deduction information is a function of the population size at the time of one of the previous impulses. A close connection to the dynamics of high-order difference equations is used to conclude that while the inclusion of a delay in the impulsive condition does not impact the optimality of the yield, sustainability may be highly affected and is generally delay-dependent. Maximal and other types of yields are explored, and sharp stability tests are obtained for the model, as well as explicit sufficient conditions. It is also shown that persistence of the solution is not guaranteed for all positive initial conditions, and extinction in finite time is possible, as is illustrated in the simulations.

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Section: Numerical Simulations and Discussionmentioning

confidence: 99%

Optimality and sustainability of delayed impulsive harvesting

Lawson,

Braverman

2022

Preprint

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“…In [10], a preypredator type fishery model with solely prey harvesting was investigated. Also many papers on prey-predator model with harvesting have been studied in [11][12][13][14][15][16][17][18][19][20][21][22]. In [23] and [24], have explored deterministic chaos vs stochastic oscillation in a prey-predator model and global stability of a three-species food chain model with diffusion, respectively.…”

Section: Introductionmentioning

confidence: 99%

A predator-prey model for the optimal control of fish harvesting through the imposition of a tax

Chatterjee¹,

Pal²

2023

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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This paper is devoted to the study of ecosystem based fisheries management. The model represents the interaction between prey and predator population with Holling II functional response consisting of different carrying capacities and constant intrinsic growth rates. We have considered the continuous harvesting of predator only. It is observed that if the intrinsic growth rate of predator population crosses a certain critical value, the system enters into Hopf bifurcation. Our observations indicate that tax, the management object in fisheries system play huge impacts on this system. The optimal harvesting policy is disposed by imposing a tax per unit of predator biomass. The optimal harvest strategy is determined using Pontryagin's maximum principle, which is subject to state equations and control limitations. The implications of tax are also examined. We have derived different bifurcations and global stability of the system. Finally, numerical simulations are used to back up the analytical results.

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“…In future work, we can continue to study the optimal harvest strategy of system (6) to explore the maximum sustainable yield and the corresponding harvest effort of system (6) [28,29]. We can also consider impulsive delayed harvesting or stage structure of prey/predator populations, which will lead to richer dynamics [30]. In addition, trying to solve system (6) using an intelligent computational solver, or different numerical methods such as the Galerkin method or Legendre wavelet algorithm will also be interesting work [31][32][33].…”

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confidence: 99%

Dynamics of a Predator–Prey Model with Impulsive Diffusion and Transient/Nontransient Impulsive Harvesting

2023

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Harvesting is one of the ways for humans to realize economic interests, while unrestricted harvesting will lead to the extinction of populations. This paper proposes a predator–prey model with impulsive diffusion and transient/nontransient impulsive harvesting. In this model, we consider both impulsive harvesting and impulsive diffusion; additionally, predator and prey are harvested simultaneously. First, we obtain the subsystems of the system in prey extinction and predator extinction. We obtain the fixed points of the subsystems by the stroboscopic map theories of impulsive differential equations and analyze their stabilities. Further, we establish the globally asymptotically stable conditions for the prey/predator-extinction periodic solution and the trivial solution of the system, and then the sufficient conditions for the permanence of the system are given. We also perform several numerical simulations to substantiate our results. It is shown that the transient and nontransient impulsive harvesting have strong impacts on the persistence of the predator–prey model.

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Stability analysis and optimal impulsive harvesting for a delayed stage-structured self dependent two compartment commercial fishery model

Cited by 6 publications

References 20 publications

Optimality and sustainability of delayed impulsive harvesting

Optimality and sustainability of delayed impulsive harvesting

A predator-prey model for the optimal control of fish harvesting through the imposition of a tax

Dynamics of a Predator–Prey Model with Impulsive Diffusion and Transient/Nontransient Impulsive Harvesting

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