International Journal of Applied Science and Engineering
Published by Chaoyang University of Technology

Xiaoning Xua and Xuncheng Huanga,b1

a Yangzhou Polytechnic University, Yangzhou, Jiangsu 225012, China.
b RDS Research Center, Infront Corp, Kearny NJ 07032, U.S.A.

 

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ABSTRACT

A three-dimensional bio-reactor model of exploitative competition of two predator organisms with inhibition responses for the same renewable organism with reproductive properties is considered. By using a Lyapunov function and the center manifold theorem the global stability, the existence of Hopf bifurcation and limit cycles are proved. This result is useful in understanding the nonlinear oscillation phenomena in bio-engineering.


Keywords: bio-reactor; center manifold theorem; Lyapunov function; Hopf bifurcation; limit cycles; nonlinear oscillation.


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ARTICLE INFORMATION



Accepted: 2007-10-31
Available Online: 2007-12-01


Cite this article:

Xu, X., Huang, X. 2007. Nonlinear oscillations in a three-dimensional competition with inhibition responses in a Bio-reactor. International Journal of Applied Science and Engineering, 5, 139–150.https://doi.org/10.6703/IJASE.2007.5(2).139

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