Dynamic analysis for a class of hydrological model with time delay under fire disturbance

In this work, we consider the dynamic properties of a class of hydrological model with time delay under fire disturbance. The stability of the equilibrium for the model, and the existence of the Hopf bifurcation are analyzed. Moreover, the direction of the Hopf bifurcation, and the stability of these periodic solutions bifurcating are derived based on the normal form and the center manifold theory. Then, the sensitivities of fire intensity and fire frequency to soil water, trees, and grasses are analyzed by the Runge-Kutta method. The result is that, fire frequency has a more significant effect on the hydrological and ecological cycle compared with fire intensity. Finally, we analyze the effect of time delay on the hydrological model through numerical simulations.