R-tipping and N-tipping in a vegetation pattern model

Vegetation in semi-arid regions has adapted to low rainfall by organizing itself in patterns, which can be described by reaction-diffusion equations that include local positive feedback (e.g. infiltration) and non-local mitigation (e.g. lateral water flow). This allows the vegetation to survive in lower rainfall conditions and creates multiple stable states, meaning that for a fixed amount of rainfall, the vegetation can exist in different patterns. It is possible to identify these different equilibrium states and to create a bifurcation diagram for the model.
As the climate changes, there is likely to be a shift in the rainfall patterns in the Sahel, although it is not yet clear if there will be an increase or decrease in precipitation. In this context, we use the vegetation pattern model and its bifurcation diagram to understand how it will respond to slow and fast changes in rainfall, and explore the possibility of rate-induced tipping (R-tipping). 
On the other hand, rainfall, land use and fires have a stochastic component, which we represent by adding two types of noise to the system: homogeneous and heterogeneous. This noise can cause a switch from one stable equilibrium to another, known as N-tipping, depending on the type of noise applied. The vegetation pattern is more stable to homogeneous noise than heterogeneous, but when it tips the homogeneous noise kill all the vegetation.
Understanding how patterned systems respond to changing environments and noise is critical for predicting the future evolution of various patterned systems globally, not just vegetation in the Sahel.
This project has received funding from the European Union’s Horizon 2020 research and innovation programme (grant no. 820970).