Analysis of a Lotka–Volterra food chain chemostat with converting time delays

作者: Fengyan Wang , Guoping Pang , Shuwen Zhang

DOI: 10.1016/J.CHAOS.2009.03.189

关键词: Control theoryFood chainChemostatComputer simulationBounded functionDiscrete time and continuous timeApplied mathematicsInstabilityAttractorMathematicsStability (probability)General Mathematics

摘要: Abstract A model of the food chain chemostat involving predator, prey and growth-limiting nutrients is considered. The incorporates two discrete time delays in order to describe involved converting processes. Lotka–Volterra type increasing functions are used species uptakes. In addition showing that solutions with positive initial conditions bounded, we establish sufficient for (i) local stability instability equilibrium (ii) global non-negative equilibria. Numerical simulation suggests have both destabilizing stabilizing effects, system can produce stable periodic solutions, quasi-periodic strange attractors.

参考文章(18)
Michael J. Bazin, Microbial population dynamics CRC Press. ,(1982)
Fengyan Wang, Chunping Hao, Lansun Chen, Bifurcation and chaos in a Monod type food chain chemostat with pulsed input and washout Chaos, Solitons & Fractals. ,vol. 31, pp. 826- 839 ,(2007) , 10.1016/J.CHAOS.2005.10.044
S. F. Ellermeyer, Competition in the chemostat: global asymptotic behavior of a model with delayed response in growth Siam Journal on Applied Mathematics. ,vol. 54, pp. 456- 465 ,(1994) , 10.1137/S003613999222522X
P. A. Taylor, P. J. LeB. Williams, Theoretical studies on the coexistence of competing species under continuous-flow conditions Canadian Journal of Microbiology. ,vol. 21, pp. 90- 98 ,(1975) , 10.1139/M75-013
A. Novick, L. Szilard, Description of the Chemostat Science. ,vol. 112, pp. 715- 716 ,(1950) , 10.1126/SCIENCE.112.2920.715
Guoping Pang, Fengyan Wang, Lansun Chen, Analysis of a Monod–Haldene type food chain chemostat with periodically varying substrate Chaos, Solitons & Fractals. ,vol. 38, pp. 731- 742 ,(2008) , 10.1016/J.CHAOS.2007.01.018
Yang Kuang, Limit cycles in a Chemostat-related model Siam Journal on Applied Mathematics. ,vol. 49, pp. 1759- 1767 ,(1989) , 10.1137/0149107
Hal Caswell, A simulation study of a time lag population model Journal of Theoretical Biology. ,vol. 34, pp. 419- 439 ,(1972) , 10.1016/0022-5193(72)90133-6
Gail S. K. Wolkowicz, Huaxing Xia, Global Asymptotic Behavior of a Chemostat Model with Discrete Delays SIAM Journal on Applied Mathematics. ,vol. 57, pp. 1019- 1043 ,(1997) , 10.1137/S0036139995287314