Bifurcation and chaos in a Tessiet type food chain chemostat with pulsed input and washout

Chaos, Solitons and Fractals

Volumn 32, Issue 4, 2007, Pages 1547-1561

  Wang, Fengyan ^a   Hao, Chunping ^a   Chen, Lansun ^b  

^a JIMEI UNIVERSITY   (China)

^b DALIAN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; CHAOS THEORY; SYSTEM STABILITY;

BOUNDARY PERIODIC SOLUTIONS; CHEMOSTAT; PERIOD-DOUBLING BIFURCATIONS; PERIODIC OSCILLATIONS;

BIFURCATION (MATHEMATICS);

EID: 33845455678     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2005.12.006     Document Type: Article

References (22)

1. Pavlou S., and Kevrekidis I.G. 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. Rinaldi S., Muratori S., and Kuznetsov Y.A. Multiple, attractors, catastrophes, and chaos in seasonally perturbed predator-prey communities. Bull Math Biol 55 (1993) 15-36
3. Kor M., Sayler G.S., and Waltman T.W. Complex dynamics in a model microbial system. Bull Math Biol 54 (1992) 619-648
4. Funasaki E., and Kor M. Invasion and chaos in periodically periodically pulsed mass-action chemostat. Theor Popul Biol 44 (1993) 203-224
5. Schaffer W.M. Can nonlinear dynamics clucidate mechanisms in ecology and epidemiology?. IMA J Math Appl Med Biol 2 (1985) 221-252
6. Cushing J.M. Two species competition in a periodic environment. J Math Biol 10 (1980) 348-400
7. Bainov D.D., and Simeonov P.S. Impulsive differential equations: periodic solutions and applications (1993), Longman, England
8. Laksmikantham V., Bainov D.D., and Simeonov P.S. Theory of impulsive differential equations (1989), World Scientific, Singapore
9. Panetta J.C. A mathematical model of periodically pulsed chemotherapy: tumor recurrence and metastasis in a competition environment. Bull Math Biol 58 (1996) 425-447
10. Shulgin B., Stone L., and Agur I. Pulse vaccination strategy in the SIR epidemic model. Bull Math Biol 60 (1998) 1-26
11. D'Onofrio A. Stability properties of pulse vaccination strategy in the SIR epidemic model. Bull Math Biol 60 (2002) 1-26
12. Liu X.N., and Chen L.S. 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. Zhang S., Dong L., and Chen L. 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., and Sun L. Permanence and complexity of a three species food chain with impulsive effect on the top predator. Int J Nonlinear Sci Numer Simul 6 2 (2005) 169-180
15. Tang S.Y., and Chen L.S. Density-dependent birth rate, birth pulse and their population dynamic consequences. J Math Biol 44 (2002) 185-199
16. Ballinger G., and Liu X. Permanence of population growth models with impulsive effects. Math Comput Modell 26 (1997) 59-72
17. Monod J. Recherches sur la croissance des cultures bactériennes (1942), Hermann, Paris
18. Cushing J.M. Periodic time-dependent predator-prey systems. SIAM J Appl Math 10 (1977) 384-400
19. May R.M. Biological populations with non-overlapping generations: stable points, stable cycles, and chaos. Science 186 (1974) 645-647
20. Gakkhar S., and Naji M.A. Order and chaos in predator to prey ratio-dependent food chain. Chaos, Solitons & Fractal 18 (2003) 229-239
21. Klebanoff A., and Hastings A. Chaos in three species food chains. J Math Biol 32 (1994) 427-451
22. Neubert M.G., and Caswell H. Density-dependent vital rates and their population dynamic consequences. J Math Biol 41 (2000) 103-121