mussel-algae model, brownian motion, regime switching, extinction, ergodic stationary distribution

Abstract

The dynamical behaviors of the quorum sensing (QS) system are closely related to the release drugs and control the PH value in microorganisms and plants. However, the effect of the main molecules AiiA, LuxI, H$ _2 $O$ _2 $, and time delayed individual and combinatorial perturbation on the QS system dynamics and the above-mentioned biological phenomena is still unclear, which are seen as a key consideration in our paper. This paper formulates a QS computational model by incorporating these several substances. First, for the protein production time delay, a critical value is given by Hopf bifurcation theory. It is found that a larger time delay can lead to a larger amplitude and a longer period. This indicates that the length of time for protein synthesis has a regulatory effect on the release of drugs from the bacterial population. Second, hen the concentrations of AiiA, LuxI, and H$ _2 $O$ _2 $ is modulated individually, the QS system undergoes periodic oscillation and bistable state. Meanwhile, oscillatory and bistable regions can be significantly affected by simultaneously perturbing any two parameters related to AiiA, LuxI, and H$ _2 $O$ _2 $. This means that the individual or simultaneous changes of the three intrinsic molecular concentrations can effectively control the drugs release and the PH value in microorganisms and plants. Finally, the sensitivity relationship between the critical value of the delay and AiiA, LuxI, H$ _2 $O$ _2 $ parameters is analyzed.

Keywords

• quorum sensing
• computational model
• combinatorial perturbation
• dynamical behaviors