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Extinction and Permanence of a Holling I Type Impulsive Predator-prey Model
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  • Journal title : Kyungpook mathematical journal
  • Volume 49, Issue 4,  2009, pp.763-770
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2009.49.4.763
 Title & Authors
Extinction and Permanence of a Holling I Type Impulsive Predator-prey Model
Baek, Hun-Ki; Jung, Chang-Do;
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 Abstract
We investigate the dynamical properties of a Holling type I predator-prey model, which harvests both prey and predator and stock predator impulsively. By using the Floquet theory and small amplitude perturbation method we prove that there exists a stable prey-extermination solution when the impulsive period is less than some critical value, which implies that the model could be extinct under some conditions. Moreover, we give a sufficient condition for the permanence of the model.
 Keywords
Predator-prey model;Holling I type functional response;impulsive differential equation;extinction;permanence;
 Language
English
 Cited by
1.
On the Dynamical Behavior of a Two-Prey One-Predator System with Two-Type Functional Responses,;

Kyungpook mathematical journal, 2013. vol.53. 4, pp.647-660 crossref(new window)
1.
On the Dynamical Behavior of a Two-Prey One-Predator System with Two-Type Functional Responses, Kyungpook mathematical journal, 2013, 53, 4, 647  crossref(new windwow)
 References
1.
G. J. Ackland and I. D. Gallagher, Stabilization of large generalized Lotka-Volterra Foodwebs by evolutionary feedback, Physical Review Letters, 93(15)(2004), 158701-1 158701-4. crossref(new window)

2.
H. Baek, Dynamic complexites of a three - species Beddington - DeAngelis system with impulsive control strategy, Acta Appl. Math., DOI 10.1007/s10440-008-9378-0. crossref(new window)

3.
H. Baek and Y. Do, Stability for a Holling type IV food chain system with impulsive perturbations, Kyungpook Math. J., 48(3)(2008), 515-527. crossref(new window)

4.
D.D. Bainov and P.S. Simeonov, Impulsive Differential Equations:Periodic Solutions and Applications, vol. 66, of Pitman Monographs and Surveys in Pure and Applied Mathematics, Longman Science & Technical, Harlo, UK, 1993.

5.
J. M. Cushing, Periodic time-dependent predator-prey systems, SIAM J. Appl. Math., 32(1977), 82-95. crossref(new window)

6.
C.S. Holling, The functional response of predator to prey density and its role in mimicry and population regulations, Mem. Ent. Sec. Can, 45(1965), 1-60.

7.
V Lakshmikantham, D. Bainov, P.Simeonov, Theory of Impulsive Differential Equations, World Scientific Publisher, Singapore, 1989.

8.
B. Liu, Y. Zhang and L. Chen, Dynamical complexities of a Holling I predator-prey model concerning periodic biological and chemical control, Chaos, Solitons and Fractals, 22(2004), 123-134. crossref(new window)

9.
Z. Lu, X. Chi and L. Chen, Impulsive control strategies in biological control and pesticide, Theoretical Population Biology, 64(2003), 39-47. crossref(new window)

10.
S. Tang, Y. Xiao, L. Chen and R.A. Cheke, Integrated pest management models and their dynamical behaviour, Bulletin of Math. Biol., 67(2005), 115-135. crossref(new window)