DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
An ordinary differential equation model describing interaction of water and plants in ecosystem is proposed. Despite its simple looking, it is shown that the model possesses surprisingly rich dynamics including multiple stable equilibria, backward bifurcation of positive equilibria, supercritical or subcritical Hopf bifurcations, bubble loop of limit cycles, homoclinic bifurcation and Bogdanov-Takens bifurcation. We classify bifurcation diagrams of the system using the rain-fall rate as bifurcation parameter. In the transition from global stability of bare-soil state for low rain-fall to the global stability of high vegetation state for high rain-fall rate, oscillatory states or multiple equilibrium states can occur, which can be viewed as a new indicator of catastrophic environmental shift.
Wang, Xiaoli; Shi, Junping; and Zhang, Guohong, INTERACTION BETWEEN WATER AND PLANTS: RICH DYNAMICS IN A SIMPLE MODEL (2017). DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 22(7).