Non-selective harvesting in prey–predator models with delay

Kar, Tapan Kumar; Pahari, U. K.

doi:10.1016/j.cnsns.2004.12.011

Cited by 42 publications

(13 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Considering the strong impact on dynamic evolution of a population (e.g., see ), Zhang et al . focused on varying harvesting rate in system and discussed the following non‐autonomous system:

({, \begin{matrix} \frac{d x (t)}{d t} = x (t) [r_{1} (t) - b (t) x (t) - \frac{a_{1} (t) y (t)}{m y^{γ} (t) + x (t)}] - c_{1} (t) x (t), \\ \frac{d y (t)}{d t} = y (t) [- r_{2} (t) + \frac{a_{2} (t) x (t)}{m y^{γ} (t) + x (t)}] - c_{2} (t) y (t), \end{matrix}) (0 < γ < 1)

where c 1 and c 2 are the harvesting coefficients of prey and predator, respectively.…”

Section: Introductionmentioning

confidence: 99%

“…In 1969, Hassell and Varley [14] introduced a general predator-prey system, in which the functional response dependents on the predator density in different way. It is called a Hassell-Varley type functional response, which take the following form: Considering the strong impact on dynamic evolution of a population (e.g., see [17][18][19][20][21]), Zhang et al [21] focused on varying harvesting rate in system (1.1) and discussed the following non-autonomous system: where c 1 and c 2 are the harvesting coefficients of prey and predator, respectively. By applying the coincidence degree theorem, the authors [21] obtained some new sufficient conditions for the existence of positive periodic solutions for system (1.2).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dynamics of a non‐selective harvesting predator–prey model with Hassell–Varley type functional response and impulsive effects

Huang

Zhang

2015

Math Methods in App Sciences

View full text Add to dashboard Cite

This paper is concerned with a non‐selective harvesting predator–prey model with Hassell–Varley type functional response and impulsive effects. By using the fixed point theory based on monotone operator, some simple conditions are obtained for the existence of at least one positive periodic solution of the model. The existence result of this paper implies that the functional response on prey does not influence the existence of positive periodic solution of the model, which completes some results given in recent years. Further, by applying the comparison theorem in impulsive differential equations and constructing a suitable Lyapunov functional, the permanence and global attractivity of the model are also investigated. The main results in this paper extend, complement, and improve the previously known result. And some examples and numerical simulations are given to illustrate the feasibility and effectiveness of the main results. Copyright © 2015 John Wiley & Sons, Ltd.

show abstract

“…Considering the strong impact on dynamic evolution of a population (e.g., see ), Zhang et al . focused on varying harvesting rate in system and discussed the following non‐autonomous system:

({, \begin{matrix} \frac{d x (t)}{d t} = x (t) [r_{1} (t) - b (t) x (t) - \frac{a_{1} (t) y (t)}{m y^{γ} (t) + x (t)}] - c_{1} (t) x (t), \\ \frac{d y (t)}{d t} = y (t) [- r_{2} (t) + \frac{a_{2} (t) x (t)}{m y^{γ} (t) + x (t)}] - c_{2} (t) y (t), \end{matrix}) (0 < γ < 1)

where c 1 and c 2 are the harvesting coefficients of prey and predator, respectively.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamics of a non‐selective harvesting predator–prey model with Hassell–Varley type functional response and impulsive effects

Huang

Zhang

2015

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…In many earlier studies, it has been shown that harvesting has a strong impact on dynamic evolution of a population, for example, see . So the study of the population dynamics with harvesting is becoming a very important subject in mathematical bio‐economics.…”

Section: Introductionmentioning

confidence: 99%

“…Under the assumption of periodicity of the coefficients of system (1.2), Wang studied the existence of at least one positive periodic solution of system (1.2) by means of Mawhin's continuation theorem of coincidence degree theory. In many earlier studies, it has been shown that harvesting has a strong impact on dynamic evolution of a population, for example, see [18][19][20][21]. So the study of the population dynamics with harvesting is becoming a very important subject in mathematical bio-economics.…”

Section: Introductionmentioning

confidence: 99%

Multiplicity of positive almost periodic solutions in a delayed Hassell-Varley-type predator-prey model with harvesting on prey

Tian-Wei-Tian

2013

Math. Meth. Appl. Sci.

View full text Add to dashboard Cite

In this paper, we consider a delayed Hassell–Varley‐type predator–prey model with harvesting on prey. By means of Mawhin's continuation theorem of coincidence degree theory, some new sufficient conditions are obtained for the existence of at least two positive almost periodic solutions for the aforementioned model. To the best of the author's knowledge, so far, the result of this paper is completely new. An example is employed to illustrate the result of this paper. Copyright © 2013 John Wiley & Sons, Ltd.

show abstract

“…Direction of Hopf bifurcation and the stability of bifurcating periodic solutions are also studied by applying the normal form theory and the center manifold theorem. Also Kar [14], Kar and Matsuda [15], Kar and Pahari [16,17], Kar and Ghorai [18], Kuang [19], and some other authors have discussed delayed predator-prey system.…”

Section: Introduction and Model Descriptionmentioning

confidence: 99%

Bifurcation Analysis of a Delayed Predator-Prey Model with Holling Type III Functional Response and Predator Harvesting

Das

Kar

2014

Journal of Nonlinear Dynamics

View full text Add to dashboard Cite

This paper tries to highlight a delayed prey-predator model with Holling type III functional response and harvesting to predator species. In this context, we have discussed local stability of the equilibria, and the occurrence of Hopf bifurcation of the system is examined by considering the harvesting effort as bifurcation parameter along with the influences of harvesting effort of the system when time delay is zero. Direction of Hopf bifurcation and the stability of bifurcating periodic solutions are also studied by applying the normal form theory and the center manifold theorem. Lastly some numerical simulations are carried out to draw for the validity of the theoretical results.

show abstract

Non-selective harvesting in prey–predator models with delay

Cited by 42 publications

References 10 publications

Dynamics of a non‐selective harvesting predator–prey model with Hassell–Varley type functional response and impulsive effects

Dynamics of a non‐selective harvesting predator–prey model with Hassell–Varley type functional response and impulsive effects

Multiplicity of positive almost periodic solutions in a delayed Hassell-Varley-type predator-prey model with harvesting on prey

Bifurcation Analysis of a Delayed Predator-Prey Model with Holling Type III Functional Response and Predator Harvesting

Contact Info

Product

Resources

About