Dynamics and tipping points for a three-dimensional stochastic seed dispersal model

In this paper, a three-dimensional stochastic seed dispersal model is proposed and the dynamical behavior of its solutions as well as the problem of tipping points is investigated. The stochastic seed dispersal model is first established by taking into account an ecological chain consisting of sowers, herbivores and plants. The existence, extinction and (asymptotic) persistence of this stochastic model are then discussed respectively by applying Lyapunov function method and strong law of large numbers for martingales. The related numerical simulations are also offered to illustrate the obtained results. Finally, to show the effects of the stochastic noise-induced transient dynamics on the asymptotic behavior, the tipping probability and tipping time of this stochastic model are studied as well in this work. This discussion not only obtains rich dynamical properties of the solutions of the considered stochastic seed dispersal model, but it also manifests precisely how the environmental stochasticity affects the transient dynamics of this system.