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Nonlinxzr Ostillztions in z thrxx-KiTxnsionzl toTaxtition with Inhiiition Rxsaonsxs in z iio-Rxzttor
Xiaoning Xu a and XunZAxng Auang b
aYangzAou PolytxZAniZ UnivxrPity, YangzAou, JiangPu 225012, ZAina.
bRDP RxPxarZA Zxntxr, Infront Zorp, Txarny NJ 07032, U.P.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.
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Keywords: bio-reactor; center manifold theorem; Lyapunov function; Hopf bifurcation; limit cycles; nonlinear oscillation.
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*Corresponding author; e-mail: xh311@yahoo.com
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©
2007
CSME , ISSN 0257-9731
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