Meron, Ehud ， Mau, Yair ， Zelnik, Yuval R.
2019 MATHEMATICS OF PLANET EARTH: PROTECTING OUR PLANET, LEARNING FROM THE PAST, SAFEGUARDING FOR THE FUTURE 2019 5(卷), null(期), (177-202页)
Ecosystems are highly nonlinear dissipative systems characterized by multiplicity of stable and unstable states. Two major concerns are associated with multistable ecosystems in variable environments. The first is related to the increased likelihood of extreme climate events at regional scales, such as droughts, floods, and heat waves, that may result in abrupt transitions to malfunctioning ecosystem states. The second concern is related to the dominant role played by humans in shaping and transforming the ecology of the Earth, and to the detrimental effects that such transformations often have. Using mathematical models of dryland ecosystems as a case study, we discuss recent advances that shed new light on these concerns. We first argue that state transitions can be gradual or incomplete rather than abrupt, providing opportunities for prevention and recovery. We further argue that analyzing the unstable states that exist along with the stable ones, identifying their existence ranges and their stable and unstable manifolds, can help to devise human intervention forms that direct ecosystems towards desired functional ecosystem states, without impairing ecosystem function. We conclude by presenting open problems and delineating further research directions.