Didactic models for tipping dynamics

Question

I would like to know if there are some toy models that describe an ecosystem dynamic (eg. ice-sheet cover, rainforest-savanna cover, permafrost thawing ) in which a critical treshold can be observed, i.e. such that depending on some parameter, or on the initial condition, the asymptotic behaviour split in one or more different state. These should be easy enough to be thought to students with basic tools of dynamical systems, but complex enough to describe the different dynamics.