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In this paper, we consider the complex dynamics of a novel mathematical model for a feedback control system of the gut microbiota, which was proposed by Dong, et al. The main work of the present paper is to study the effect of antibiotics injection on the gut microbiota through some dynamical methods, such as double Hopf bifurcation analysis and so on. We first use DDE-BIFTOOL to find the non-resonant double Hopf bifurcation points of the system, and draw the bifurcation diagram with two bifurcation parameters, τ 1 and τ 2 , i.e., respective measurement delays. Then we study small perturbations of two delay differential equations at these double Hopf bifurcation points, and the method of multiple scales is employed to obtain two common complex amplitude equations. By analyzing the amplitude equations, we can derive the classification and unfolding of these double Hopf bifurcation points. Finally, we verify the results by numerical simulations. We find more complicated dynamic behaviors of the system via analytical method. For example, there exists stable equilibrium, stable periodic solution or even the co-existing stable periodic solutions in respective region. And the numerical simulations are consistent with the analytic results, meanwhile it implies that the MMS is effective and accurate. All complex dynamical phenomena found in the present paper can be very helpful for the researchers to understand the mechanism of the system of gut microbiota. And it is also very significant to microbiology and engineering control. It reveals that the measurement delays can induce the complicated dynamics in this system and to the ends of excellent performance, we should take the proper values of these delays. • Find complicated behaviors in delayed gut microbiota system esp. bi-stability. • Measurement delays can induce complicated dynamics and careful to take values. • Complicated behaviors be very helpful to understand mechanism of gut mocrobiota. [ABSTRACT FROM AUTHOR]

• We developed cellular automaton model on social forces interaction in building evacuation. • The cellular automaton model was verified using experimental data. • Clustering attraction always increased evacuation time regardless of other factors. • Repulsive force of obstacles played negligible roles on the evacuation time. • Evacuation path can be optimized by adjusting social forces to reduce evacuation time. A basic cellular automaton model does not consider social forces interaction in building evacuation thus could not explain complex crowd evacuation processes. This study developed a cellular automaton model on social forces interaction in building evacuation, where the positive and negative impacts of social forces on evacuation time were simulated and analyzed. The model was verified using experimental data. The clustering attraction between people always increased the evacuation time regardless of the number of evacuees, the building size, the number of exits, and the people distribution, thus the clustering attraction is always to be avoided. When people in a room were randomly and evenly distributed, the repulsive force of obstacles, the attractiveness of evacuation direction, and the repulsive force of exit congestion played negligible roles on the evacuation time thus could be ignored. The evacuation path could be optimised by adjusting the influence coefficients of social forces to reduce the evacuation time. [ABSTRACT FROM AUTHOR]