Department of Mathematical and Physics, Shijiazhuang Tiedao University, 050043, China.
Department of Mathematical and Physics, Shijiazhuang Tiedao University, 050043, China.
Biosystems. 2021 Mar;201:104329. doi: 10.1016/j.biosystems.2020.104329. Epub 2020 Dec 24.
We study the dynamic growth behaviors of Bacillus subtilis biofilms by using a stochastic delay differential equation similar to the Mackey-Glass equation. We observe a wealth of dynamic behavior from a mathematical perspective. Firstly, the change of the time delay (i.e. the time that the growth state of the periphery to affect the stress of the interior cells needs and the time required for the stress signal coming from the interior to reach the peripheral cells) and the external excitation (i.e. the change in temperature) frequency will influence the size of Bacillus subtilis biofilm and the collective growth of the cell community. We also found the resonance phenomena in mathematics, which is of great help in understanding the behavior of stress levels in the biofilm periphery. Secondly, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by using the normal form theory and the center manifold reduction. Numerical simulations are carried out to ensure theoretical results. Finally, the effects of noise on stress levels in the biofilm periphery are analyzed and reveal more complex dynamics of the system.
我们通过使用类似于 Mackey-Glass 方程的随机时滞微分方程来研究枯草芽孢杆菌生物膜的动态生长行为。从数学角度观察到了丰富的动态行为。首先，时滞（即外围生长状态影响内部细胞压力所需的时间以及内部压力信号到达外围细胞所需的时间）和外部激励（即温度变化）频率的变化会影响枯草芽孢杆菌生物膜的大小和细胞群落的集体生长。我们还发现了数学中的共振现象，这对理解生物膜外围的压力水平行为有很大帮助。其次，利用规范形理论和中心流形约化推导出 Hopf 分岔的方向和分岔周期解的稳定性。通过数值模拟来保证理论结果。最后，分析了噪声对生物膜外围压力水平的影响，揭示了系统更复杂的动力学。
