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Hopf Bifurcations of a Chemostat System with Bi-parameters

Hopf Bifurcations of a Chemostat System with Bi-parameters
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摘要 We study a chemostat system with two parameters, So-initial density and D-flow-speed of the solution. At first, a generalization of the traditional Hopf bifurcation theorem is given. Then, an existence theorem for the Hopf bifurcation of the chemostat system is presented. We study a chemostat system with two parameters, So-initial density and D-flow-speed of the solution. At first, a generalization of the traditional Hopf bifurcation theorem is given. Then, an existence theorem for the Hopf bifurcation of the chemostat system is presented.
出处 《Northeastern Mathematical Journal》 CSCD 2004年第2期167-174,共8页 东北数学(英文版)
基金 The NSF (10171010) of China Major Project of Education Ministry (01061) of China.
关键词 Hopf bifurcation chemostat system EQUILIBRIA Hopf bifurcation, chemostat system, equilibria
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参考文献5

  • 1Freedman, H.I., Joseph, W.H. So, and Paul Waltman, Coexistence in a model of competition in the ehemostat incorporating discrete delays, SIAM J. Appl. Math., 49(3)(1989),859-870.
  • 2Li X. G., Pan J. Q. and Huang Q. C., Hopf bifurcation analysis of some modified chemostar models, Northeast. Math. J., 14(4)(1998), 392-400.
  • 3Li X. Y., Bai L., Yang F. and Huang Q. C., Hopf bifurcation analysis of the chemostat models, J. Northeast Normal Univ., 32(3)(2000), 6-12.
  • 4Hassard, B. D., Kazarinoff, N. D. and Wan Y. H., Theory and Applications of Hopf Bifurdation, Cambridge Univ. Press, London, 1981.
  • 5Hale, J. K., Theory of Functional Differential Equations, Springer-Varlag, New York,1977.

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