Bifurcation and complexity of Monod type predator-prey system in a pulsed chemostat

Chaos, Solitons and Fractals

Volumn 27, Issue 2, 2006, Pages 447-458

  Wang, Fengyan ^a,b   Zhang, Shuwen ^c   Chen, Lansun ^a   Sun, Lihua ^a  

^a DALIAN UNIVERSITY OF TECHNOLOGY   (China)

^b Northern Nationalities University   (China)

^c ANSHAN NORMAL UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

CHEMOSTATS; COMPUTATIONAL COMPLEXITY; DIFFERENTIAL EQUATIONS; DISEASES; MATHEMATICAL MODELS; OSCILLATIONS;

BIFURCATION THEORY; IMPULSED DIFFERENTIAL EQUATIONS (IDE); PREDATOR; PULSED CHEMOSTAT;

BIFURCATION (MATHEMATICS);

EID: 22844435930     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2005.04.025     Document Type: Article

References (22)

1. S. Pavlou, and I.G. Kevrekidis Microbial predation in a periodically operated chemostat: a global study of the interaction between natural and externally imposed frequencies Math Biosci 108 1992 1 55
2. S. Rinaldi, S. Muratori, and Y.A. Kuznetsov Multiple, attracto, catastrophes, and chaos in seasonally perturbed predator-prey communities Bull Math Biol 55 1993 15 36
3. M. Kor, G.S. Sayler, and T.W. Waltman Complex dynamics in a model microbial system Bull Math Biol 54 1992 619 648
4. E. Funasaki, and M. Kor Invasion and chaos in periodically pulsed mass-action chemostat Theor Populat Biol 44 1993 203 224
5. W.M. Schaffer Can nonlinear dynamics clucidate mechanisms in ecology and epidemiology? IMA J Math Appl Med Biol 2 1985 221 252
6. J.M. Cushing Two species competition in a periodic enviroment J Math Biol 10 1980 348 400
7. Bainov D, Simeonor P. Impulsive differential equations: Periodic solutions and applications. Pitman Monographs and Surreys in Pure and Applied Mathematics, 1993. p. 66.
8. V. Laksmikantham, D.D. Bainov, and P.S. Simeonov Theory of impulsive differential equations 1989 World Scientific Singapore
9. J.C. Panetta A mathematical model of periodically pulsed chemotherapy: tumor recurrence and metastasis in a competition environment Bull Math Biol 58 1996 425 447
10. B. Shulgin, L. Stone, and I. Agur Pulse vaccination strategy in the SIR epidemic model Bull Math Biol 60 1998 1 26
11. A. D'Onofrio Stability properties of pulse vaccination strategy in the SIR epidemic model Bull Math Biol 60 2002 1 26
12. X.N. Liu, and L.S. Chen Complex dynamics of Holling type II Lotka-Volterra predator-prey system with impulsive perturbations on the predator Chaos, Solitons & Fractals 16 2003 311 320
13. S. Zhang, L. Dong, and L. Chen The study of predator-prey system with defensive ability of prey and impulsive perturbations on the predator Chaos, Solitons & Fractals 23 2005 631 643
14. Wang F, Zhang S, Chen L, Sun L. Permanence and complexity of a three species food chain with impulsive effect on the top predator. Int J Nonlinear Sci Numer Simul, 2005.
15. S.Y. Tang, and L.S. Chen Density-dependent birth rate, birth pulse and their population dynamic consequences J Math Biol 44 2002 185 199
16. G. Ballinger, and X. Liu Permanence of population growth models with impulsive effects Math Comput Modell 26 1997 59 72
17. J. Monod Recherches sur la croissance des cultures bactériennes 1942 Hermann Paris
18. J.M. Cushing Periodic time-dependent predator-prey systems SIAM J Appl Math 10 1977 384 400
19. R.M. May Biological populations with non-overlapping generations: Stable points, stable cycles, and chaos Science 186 1974 645 647
20. S. Gakkhar, and M.A. Naji Order and chaos in predator to prey ratio-dependent food chain Chaos, Solitons & Fractal 18 2003 229 239
21. A. Klebanoff, and A. Hastings Chaos in three species food chains J Math Biol 32 1994 427 451
22. M.G. Neubert, and H. Caswell Density-dependent vital rates and their population dynamic consequences J Math Biol 41 2000 103 121