Impulsive harvesting and stocking in a Monod–Haldane functional response predator–prey system

Liu, Zhijun; Tan, Renxiang

doi:10.1016/j.chaos.2006.03.054

Cited by 76 publications

(44 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Optimal harvesting problem have been studied in environmental and renewable resource economics. A lot of good work on this topic is emerged in recent years (see [13,14,15,16,17,18,19] in detail). Song and Chen [15] researched a competitive population model of two species with harvesting.…”

Section: Preprintmentioning

confidence: 99%

Incorporating prey refuge into a predator–prey system with imprecise parameter estimates

et al. 2015

Self Cite

View full text Add to dashboard Cite

This article concerns with the optimal harvesting of a predator-prey model with prey refuge and imprecise biological parameters. We consider the above model under impreciseness and introduce parametric functional form of an interval which are different from that of models with precise biological parameters. We study the existence and stability of the equilibria. The bionomic equilibria of the model are discussed. Also, the optimal harvesting policy is derived by using Pontryagin's maximal principle. Numerical simulations are presented to verify the feasibility of our analytical results.

show abstract

Section: Preprintmentioning

confidence: 99%

Incorporating prey refuge into a predator–prey system with imprecise parameter estimates

et al. 2015

Self Cite

View full text Add to dashboard Cite

show abstract

“…Numerous examples were given in Bainov's and his collaborators' books [4,5]. Some impulsive differential equations have been recently introduced in population dynamics and neural network, such as population ecology [6--13], harvesting and stocking [14], birth pulse [15], vaccination [16,17], chemostat [18], chemotherapeutic treatment of disease [19], and artificial neural network [20].…”

Section: (T) = X(t)[a(t)−b(t)x(t)]− C(t)x 2 (T) D(t)+x 2 (T)mentioning

confidence: 99%

Permanence in a periodic single species system subject to linear/constant impulsive perturbations

Liu

Tang

Qin

et al. 2010

Math. Meth. Appl. Sci.

Self Cite

View full text Add to dashboard Cite

In this paper, a single species system with linear/constant impulsive perturbations is established. The linear and constant impulses are realized at fixed moments of time. By using the comparison principle of impulsive differential equations and analysis techniques, sufficient conditions for the permanence of the system with linear and constant impulsive perturbations are obtained, respectively. Numerical simulations are presented to substantiate our analytical results, and show that the impulsive perturbations play a crucial role.

show abstract

“…In recent years, the optimal management of renewable resources, which has a direct relationship to sustainable development, has been studied extensively by many authors [2][3][4][5][6]. Especially, the predator-prey models with continuous harvesting are investigated by many papers [7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a periodic switched predator–prey system with hibernation, birth pulse and impulsive harvesting

Tang

Jiao

2015

J. Appl. Math. Comput.

View full text Add to dashboard Cite

In this work, a periodic impulsive switched system is employed to describe the effect of impulsive birth and harvesting on predator-prey dynamics with hibernation in prey population. We show that if some conditions are satisfied, the predator-extinction boundary periodic solution of the investigated system is the globally asymptotically stable. We also show that if one certain condition is satisfied, the investigated system is permanent. Finally, the numerical analysis are also employed to illustrate the results. Our results provide a strategic decision for the biological economics management.

show abstract

Impulsive harvesting and stocking in a Monod–Haldane functional response predator–prey system

Cited by 76 publications

References 14 publications

Incorporating prey refuge into a predator–prey system with imprecise parameter estimates

Incorporating prey refuge into a predator–prey system with imprecise parameter estimates

Permanence in a periodic single species system subject to linear/constant impulsive perturbations

Dynamics of a periodic switched predator–prey system with hibernation, birth pulse and impulsive harvesting

Contact Info

Product

Resources

About