The dynamics of eco-systems and, in particular, their response to climatic changes and anthropogenic disturbances are of great interest and importance. An example of such dynamics is the desertification process that many areas are undergoing, which is a major concern over the last decades. This process is often studied by describing the dynamics of dry-land vegetation.
The various feedbacks in most eco-systems allow for the response to be in the form of an abrupt (catastrophic) regime shift which has been discussed extensively in the literature.
Non-linear dynamics and pattern formation theories predict many possibilities for the response of spatially extended eco-systems, such as dry-land vegetation, to climatic changes and anthropogenic disturbances and we investigated the validity and applicability of these scenarios in arid-land vegetation models.
We show that the classic view of bi-stability does not fully capture the possible states of the system, due to multiplicity of pattern wave-length, and the occurrence of localized states in the system. Further, we do not find evidence of the possibility of an invasion of a bare-soil state front, i.e., expansion of the bare soil into the patterned area, in any of these models.
This leads us to consider the possibility of incipient transitions between many different stable states in the system, and discuss the occurrence of a desertification process as a process of front dynamics and/or gradual transition.