Dynamic complexities of a three-species Beddington-DeAngelis system with impulsive control strategy

Acta Applicandae Mathematicae

Volumn 110, Issue 1, 2010, Pages 23-38

  Baek, Hunki ^a  

^a Kyungpook National University   (South Korea)

Author keywords

Beddington DeAngelis functional response; Floquet theory; Impulsive differential equations; Three species food systems

Indexed keywords

BEDDINGTON-DE ANGELIS FUNCTIONAL RESPONSE; COMPARISON THEOREM; COMPLEX DYNAMIC BEHAVIOR; DYNAMIC COMPLEXITY; DYNAMICAL PROPERTIES; FLOQUET THEORY; FOOD CHAIN SYSTEM; FOOD SYSTEM; IMPULSIVE CONTROL STRATEGY; IMPULSIVE DIFFERENTIAL EQUATION; NUMERICAL EXAMPLE; PERIODIC SOLUTION; SMALL AMPLITUDE PERTURBATIONS;

CHAINS; PERTURBATION TECHNIQUES;

DIFFERENTIAL EQUATIONS;

EID: 77952089555     PISSN: 01678019     EISSN: 15729036     Source Type: Journal    
DOI: 10.1007/s10440-008-9378-0     Document Type: Article

References (32)

1. Baek, H.: Extinction and permanence of a three species Lotka-Volterra system with impulsive control strategies. Discrete Dyn. Nat. Soc., vol. 2008, Article ID 752403, 18 p. doi: 10.1155/2008/752403
2. H. Baek H.H. Lee 2008 Permanence of a three-species food chain system with impulsive perturbations Kyungpook Math. J. 48 3 503 514 1167.34305 2454692
3. Bainov, D.D., Simeonov, P.S.: Impulsive Differential Equations: Periodic Solutions and Applications. Pitman Monographs and Surveys in Pure and Applied Mathematics, vol. 66. Longman, Harlow (1993)
4. J.R. Beddington 1975 X Mutual interference between parasites or predator and its effect on searching efficiency J. Anim. Ecol. 44 331 340 10.2307/3866
5. D.L. DeAngelis R.A. Goldstein R.V. O'Neill 1975 A model for trophic interaction Eocolgy 56 881 892 10.2307/1936298
6. C. Cosner D.L. DeAngelis 1999 Effects of spatial grouping on the functional response of predators Theor. Popul. Biol. 56 65 75 0928.92031 10.1006/tpbi.1999.1414 (Pubitemid 29395865)
7. M. Fan Y. Kuang 2004 Dynamics of a nonautonomous predator-prey system with the Beddington-DeAngelis functional response J. Math. Anal. Appl. 295 15 39 1051.34033 10.1016/j.jmaa.2004.02.038 2064405 (Pubitemid 38939353)
8. H.I. Freedman R.M. Mathsen 1993 Persistence in predator-prey systems with ratio-dependent predator influence Bull. Math. Biol. 55 4 817 827 0771.92017
9. T.-W. Hwang 2003 Global analysis of the predator-prey system with Beddington-DeAngelis functional response J. Math. Anal. Appl. 281 395 401 1033.34052 1980099 (Pubitemid 36802637)
10. T.-W. Hwang 2004 Uniqueness of limit cycles of the predator-prey system with Beddington-DeAngelis functional response J. Math. Anal. Appl. 290 113 122 1086.34028 10.1016/j.jmaa.2003.09.073 2032229 (Pubitemid 38236206)
11. G. Jiang Q. Lu L. Peng 2005 Impulsive ecological control of a stage-structured pest management system Math. Biosci. Eng. 2 2 329 344 1082.34005 2144243
12. Lakshmikantham, V., Bainov, D., Simeonov, P.: Theory of Impulsive Differential Equations. World Scientific, Singapore (1989)
13. Z. Li W. Wang H. Wang 2006 The dynamics of a Beddington-type system with impulsive control strategy Chaos Solitons Fractals 29 1229 1239 1142.34305 10.1016/j.chaos.2005.08.195 2227684 (Pubitemid 44671758)
14. B. Liu Y. Zhang L. Chen 2005 Dynamic complexities in a Lotka-Volterra predator-prey model concerning impulsive control strategy Int. J. Bifurc. Chaos 15 2 517 531 1080.34026 10.1142/S0218127405012338 2143622 (Pubitemid 40661906)
15. B. Liu Z. Teng L. Chen 2006 Analysis of a predator-prey model with Holling II functional response concerning impulsive control strategy J. Comput. Appl. Math. 193 1 347 362 1089.92060 10.1016/j.cam.2005.06.023 2228722
16. B. Liu Y.J. Zhang L.S. Chen L.H. Sun 2005 The dynamics of a prey-dependent consumption model concerning integrated pest management Acta Math. Sin. Engl. Ser. 21 3 541 554 1094.34030 10.1007/s10114-004-0476-2 2145907 (Pubitemid 40937181)
17. X. Liu L. Chen 2003 Complex dynamics of Holling type II Lotka-Volterra predator-prey system with impulsive perturbations on the predator Chaos Solitons Fractals 16 311 320 1085.34529 10.1016/S0960-0779(02)00408-3 1949478 (Pubitemid 35412184)
18. K. Negi S. Gakkhar 2007 Dynamics in a Beddington-DeAngelis prey-predator system with impulsive harvesting Ecol. Model. 206 421 430 10.1016/j.ecolmodel. 2007.04.007 (Pubitemid 47081331)
19. G.T. Skalski J.F. Gilliam 2001 Functional responses with predator interference: viable alternatives to the Holling type II mode Ecology 82 3083 3092 10.1890/0012-9658(2001)082[3083:FRWPIV]2.0.CO;2
20. W. Wang H. Wang Z. Li 2008 Chaotic behavior of a three-species Beddington-type system with impulsive perturbations Chaos Solitons Fractals 37 438 443 10.1016/j.chaos.2006.09.013 2402636 (Pubitemid 351380470)
21. S. Tang R.A. Cheke 2005 State-dependent impulsive models of integrated pest management (IPM) strategies and their dynamic consequences J. Math. Biol. 50 257 292 1080.92067 10.1007/s00285-004-0290-6 2135823 (Pubitemid 40383674)
22. S. Tang Y. Xiao L. Chen R.A. Cheke 2005 Integrated pest management models and their dynamical behaviour Bull. Math. Biol. 67 115 135 10.1016/j.bulm.2004. 06.005 2204249 (Pubitemid 40181071)
23. Wang, W.B., Shen, J.H., Nieto, J.J.: Permanence periodic solution of predator prey system with Holling type functional response and impulses. Discrete Dyn. Nat. Soc. (2007). Article ID 81756, 15 p.
24. W. Wang H. Wang Z. Li 2007 The dynamic complexity of a three-species Beddington-type food chain with impulsive control strategy Chaos Solitons Fractals 32 1772 1785 05238644 10.1016/j.chaos.2005.12.025 2299091 (Pubitemid 46136967)
25. J. Yan A. Zhao J.J. Nieto 2004 Existence and global attractively of positive periodic solution of periodic single-species impulsive Lotka-Volterra systems Math. Comput. Model. 40 509 518 1112.34052 10.1016/j.mcm.2003.12.011 2102205 (Pubitemid 40172108)
26. S. Zhang L. Chen 2005 A Holling II functional response food chain model with impulsive perturbations Chaos Solitons Fractals 24 1269 1278 1086.34043 10.1016/j.chaos.2004.09.051 2123273 (Pubitemid 40206053)
27. S. Zhang L. Chen 2006 A study of predator-prey models with the Beddington-DeAngelis functional response and impulsive effect Chaos Solitons Fractals 27 237 248 1102.34032 10.1016/j.chaos.2005.03.039 2165278 (Pubitemid 40999980)
28. S. Zhang L. Dong L. Chen 2005 The study of predator-prey system with defensive ability of prey and impulsive perturbations on the predator Chaos Solitons Fractals 23 631 643 1081.34041 10.1016/j.chaos.2004.05.044 2089665 (Pubitemid 43062481)
29. S. Zhang D. Tan L. Chen 2006 Dynamic complexities of a food chain model with impulsive perturbations and Beddington-DeAngelis functional response Chaos Solitons Fractals 27 768 777 1094.34031 10.1016/j.chaos.2005.04.047 2166420 (Pubitemid 41084209)
30. S. Zhang D. Tan L. Chen 2006 Chaotic behavior of a chemostat model with Beddington-DeAngelis functional response and periodically impulsive invasion Chaos Solitons Fractals 29 474 482 1121.92070 10.1016/j.chaos.2005.08.026 2211482 (Pubitemid 43152216)
31. S. Zhang D. Tan L. Chen 2006 Chaotic behavior of a periodically forced predator-prey system with Beddington-DeAngelis functional response and impulsive perturbations Adv. Complex Systems 9 3 209 222 05133554 10.1142/ S0219525906000811 2283041 (Pubitemid 44877960)
32. Q. Zhipeng Y. Jun Z. Yun 2004 The asymptotic behavior of a chemostat model with the Beddington-DeAngelis functional response Math. Biosci. 187 175 187 1049.92039 10.1016/j.mbs.2003.10.001 2043824 (Pubitemid 38096339)