Publisher : Department of Mathematics, Kyungpook National University
DOI : 10.5666/KMJ.2008.48.3.515
Title & Authors
Stability for a Holling Type IV Food Chain System With Impulsive Perturbations Baek, Hunki; Do, Young-Hae;
We investigate a three species food chain system with a Holling type IV functional response and impulsive perturbations. We find conditions for local and global stabilities of prey(or predator) free periodic solutions by applying the Floquet theory and the comparison theorems.
three-species food chain systems;Holling type IV functional response;impulsive differential equations;Floquet thoery;
Extinction and Permanence of a Holling I Type Impulsive Predator-prey Model, Kyungpook mathematical journal, 2009, 49, 4, 763
Impulsive Perturbations of a Three-Species Food Chain System with the Beddington-DeAngelis Functional Response, Discrete Dynamics in Nature and Society, 2012, 2012, 1
Complex Dynamical Behaviors in a Predator-Prey System with Generalized Group Defense and Impulsive Control Strategy, Discrete Dynamics in Nature and Society, 2013, 2013, 1
Seasonal Effects on a Beddington-DeAngelis Type Predator-Prey System with Impulsive Perturbations, Abstract and Applied Analysis, 2009, 2009, 1
DYNAMICS OF A STAGE-STRUCTURED PREDATOR-PREY MODEL CONCERNING IMPULSIVE CONTROL STRATEGY, Journal of Biological Systems, 2009, 17, 04, 779
Permanence and stability of an Ivlev-type predator–prey system with impulsive control strategies, Mathematical and Computer Modelling, 2009, 50, 9-10, 1385
R. Arditi and L. R. Ginzburg, Coupling in predator-prey dynamics:Ratio-dependence, J. Theor. Biol., 139(1989), 311-326.
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. B. Collings, The effects of the functional response on the bifurcation behavior of a mite predator-prey interaction model, J. Math. Biol., 36(1997), 149-168.
C. Cosner, D. L. DeAngelis, Effects of spatial grouping on the functional response of predators, Theoretical Popuation Biology, 56(1999), 65-75.
H. I. Freedman and R. M. Mathsen, Persistence in predator-prey systems with ratiodependent predator influence, Bulletin of Math. Biology, 55(4)(1993), 817-827.
M. P. Hassell and G. C. Varley, New inductive population model for insect parasites and its bearing on biological control, Nature, 223(1969), 1133-1136.
S.-B. Hsu and T.-W. Huang, Global stability for a class of predator-prey systems, SIAM J. Appl. Math., 55(3)(1995), 763-783.
K. Kitamura, K. Kashiwagi, K.-i. Tainaka, T. Hayashi, J. Yoshimura, T. Kawai and T. Kajiwara, Asymmetrical effect of migration on a prey-predator model, Physics Letters A, 357(2006), 213-217.
V Lakshmikantham, D. Bainov, P.Simeonov, Theory of Impulsive Differential Equations, World Scientific Publisher, Singapore, 1989.
B. Liu, Z. Teng and L. Chen, Analsis of a predator-prey model with Holling II functional response concerning impulsive control strategy, J. of Comp. and Appl. Math., 193(1)(2006), 347-362
B. Liu, Y. J. Zhang, L. S. Chen and L. H. Sun, The dynamics of a prey-dependent consumption model concerning integrated pest management, Acta Mathematica Sinica, English Series, 21(3)(2005), 541-554.
X. Liu and L. Chen, Complex dynamics of Holling type II Lotka-Volterra predator-prey system with impulsive perturbations on the predator, Chaos, Solitons and Fractals, 16(2003), 311-320.
P. Georgescu and G. Morosanu, Impulsive perturbations of a three-trophic prey-dependent food chain system, Mathematical and Computer Modeling(2008), doi:10.1016/j.mcm.2007.12.006.
S. Ruan and D. Xiao, Global analysis in a predator-prey sytem with non-monotonic functional response, SIAM J. Appl. Math., 61(4)(2001), 1445-1472.
E, Saez and E. Gonzalez-Olivares, Dynamics of a predator-prey model, SIAM J. Appl. Math., 59(5)(1999), 1867-1878.
G. T. Skalski and J. F. Gilliam, Funtional responses with predator interference: viable alternatives to the Holling type II mode, Ecology, 82(2001), 3083-3092.
W. Wang, H. Wang and Z. Li, Chaotic behavior of a three-species Beddington-type system with impulsive perturbations, Chaos Solitons and Fractals, 37(2008), 438-443.
S. Zhang and L. Chen, Chaos in three species food chain system with impulsive perturbations, Chaos Solitons and Fractals, 24(2005), 73-83.
S. Zhang and L. Chen, A Holling II functional response food chain model with impulsive perturbations, Chaos Solitons and Fractals, 24(2005), 1269-1278.
S. Zhang, F. Wang and L. Chen, A food chain model with impulsive perturbations and Holling IV functional response, Chaos, Solitons and Fractals, 26(2005), 855-866.
Y. Zhang, B. Liu and L. Chen, Extinction and permanence of a two-prey one-predator system with impulsive effect, Mathematical Medicine and Biology, 20(2003), 309-325.