Oscillatory Dynamics Induced by Time Delays in the Quorum Sensing System of Pseudomonas Aeruginosa.

In this work, a sufficiently simple quorum sensing model allows one to perform detailed analytic studies to gain insights into the dynamical mechanisms in Pseudomonas aeruginosa. It is shown that an optimal rate of model parameters is essential to induce oscillations without considering time delays. Theoretical analysis and numerical simulation reveal that the delays can induce subcritical Hopf bifurcation and oscillation hysteresis. By using the center manifold and normal form theory, the explicit formulas for determining the stability and direction of periodic solutions bifurcating from Hopf bifurcations are derived. Numerical results show that the global periodic solutions bifurcating from the equilibrium exist when the delay is faraway from the first critical value. Moreover, the length of the delay can determine the amplitudes and the periods of the oscillations. A two-parameter diagram of delays is given to illustrate their crucial roles in coordinating and regulating oscillatory dynamics of the system. These results may help to further understand the dynamics of quorum sensing system in Pseudomonas aeruginosa and provide beneficial guidelines in the process of bacterial delivery of drugs. [ABSTRACT FROM AUTHOR]