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Bifurcation in the stable manifold of a chemostat with general polynomial yields
Author(s) -
Zhu Lemin,
Huang Xuncheng
Publication year - 2010
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1174
Subject(s) - mathematics , chemostat , bifurcation , limit (mathematics) , center manifold , polynomial , hopf bifurcation , manifold (fluid mechanics) , stability (learning theory) , order (exchange) , mathematical analysis , physics , computer science , nonlinear system , mechanical engineering , genetics , finance , quantum mechanics , machine learning , bacteria , engineering , economics , biology
A three‐dimensional chemostat with n th‐ and m th‐order polynomial yields, instead of the particular ones such as A + BS , A + BS 2 , A + BS 3 , A + BS 4 , A + BS 2 + CS 3 , and A + BS n , is proposed. The existence of limit cycles in the two‐dimensional stable manifold, the Hopf bifurcation, and the stability of the periodic solution created by the bifurcation is proved. Copyright © 2009 John Wiley & Sons, Ltd.