一类具有信号分子调节作用的非连续模型的动力学性质

数学物理学报 ›› 2019, Vol. 39 ›› Issue (6): 1545-1554.

一类具有信号分子调节作用的非连续模型的动力学性质

王茹,张仲华*(),刘叶玲

西安科技大学理学院西安 710054

收稿日期:2018-07-31 出版日期:2019-12-26 发布日期:2019-12-28
通讯作者: 张仲华 E-mail:941439353@qq.com
基金资助:
陕西省自然科学基金(2015JM1011)

Dynamical Properties of a Discontinuous Models with Signal Molecules Regulation

Ru Wang,Zhonghua Zhang*(),Yeling Liu

School of Sciences, Xi'an University of Science and Technology, Xi'an 710054

Received:2018-07-31 Online:2019-12-26 Published:2019-12-28
Contact: Zhonghua Zhang E-mail:941439353@qq.com
Supported by:
the Natural Science Foundation of Shaanxi Province(2015JM1011)

摘要/Abstract

摘要：

将信号分子的浓度作为指标，建立了一类描述病菌群体感应机理对信号分子浓度调节的非连续模型，讨论了模型滑动模块区域的存在性，真（假）平衡点和伪平衡点的存在性及稳定性.特别地，证明了穿越极限环的存在性.最后，运用Matlab软件进行数值模拟，支撑了理论结果.

关键词: 群体感应, 非连续模型, 滑模动力学, 极限环, 稳定性

Abstract:

In this paper, the concentration of signal molecules is used as an indicator to establish a discontinuous model that describes the regulation of signal molecules concentration by the quorum sensing mechanism of pathogens. The existence of the sliding module region, the existence and stability of the true (false) equilibrium point and the pseudo equilibrium point are discussed. In particular, the existence of the crossing limit cycles is proved. Finally, the Matlab software is used to carry out numerical simulations to support the theoretical results.

Key words: Quorum sensing, Discontinuous model, Sliding mode dynamics, Limit cycles, Stability

中图分类号:

O175

王茹,张仲华,刘叶玲. 一类具有信号分子调节作用的非连续模型的动力学性质[J]. 数学物理学报, 2019, 39(6): 1545-1554.

Ru Wang,Zhonghua Zhang,Yeling Liu. Dynamical Properties of a Discontinuous Models with Signal Molecules Regulation[J]. Acta mathematica scientia,Series A, 2019, 39(6): 1545-1554.

图/表 11

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参考文献 11

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参数	值	参数	值
$\alpha$	0.10564	$\rho $	50
$\gamma $	10	$\omega$	10
$\delta $	30	$k$	0.003
$\delta $	1.0564

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