April 23, 2004; 2:00-3:00pm (talk), 3:00-5:00pm (discussion)

Eli Lilly
Institute of Molecular Biology, California Institute of Technology

(April 23, 2004 2:00 PM - 5:00 PM)

April 23, 2004; 2:00-3:00pm (talk), 3:00-5:00pm (discussion)

Abstract

Specifcally, the talk will include: 1) Formulation and stability analysis of the variable yield model; 2) A subcritical bifurcation lemma, divergence criterion; 3) Several examples involving the divergence criterion; and 4) Examples of complicated dynamics for two competitors, period-doubling cascades, Neimark-Sacker bifurcation.

    References:
  • Pilyugin, S.S., & Waltman, P. (2003). Multiple limit cycles in the chemostat with variable yield. Math. Biosci., 182 , 151-166.
  • Pilyugin, S.S., & Waltman, P. (2003). Divergence criterion for generic planar systems. SIAM Journal on Applied Mathematics, 64 (1), 81-93.
  • Arino, J., Pilyugin, S.S., & Wolkowicz, G. S. K. Considerations on yield, nutirent uptake, cellular growth, and competition in chemostat models. Manuscript submitted for publication.