To characterize the competition between immune cells and bacteria, a microcosmic dynamical model with delayed quorum sensing mechanism is constructed. According to the Liapunov staiblity theory, the center manifold theorem and the norm form theory, local and global stability of the bacteria free equilibrium, existence and globally asymptotical stability of the positive equilibrium, and stability of the nonhyperbolic bacteria free equilibrium are studied for any positive delay.
ZHANG Zhong-hua1, MENG Qing-xun2, SUO Yao-hong1
. Stability of a Delayed Model with the Mechanism of Information Exchange[J]. Journal of Shanghai University, 2013
, 19(3)
: 308
-314
.
DOI: 10.3969/j.issn.1007-2861.2013.03.017
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