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;
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.
Predator-prey model;Holling I type functional response;impulsive differential equation;extinction;permanence;
On the Dynamical Behavior of a Two-Prey One-Predator System with Two-Type Functional Responses, Kyungpook mathematical journal, 2013, 53, 4, 647
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.
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.
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.
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.
J. M. Cushing, Periodic time-dependent predator-prey systems, SIAM J. Appl. Math., 32(1977), 82-95.
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.
V Lakshmikantham, D. Bainov, P.Simeonov, Theory of Impulsive Differential Equations, World Scientific Publisher, Singapore, 1989.
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.
Z. Lu, X. Chi and L. Chen, Impulsive control strategies in biological control and pesticide, Theoretical Population Biology, 64(2003), 39-47.
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.