There are many ecological evidences that regular vegetation patterns in semi-arid regions may be interpreted has early warning signals of catastrophic transitions to an irreversible homogeneous bare-soil state (desertification). In this framework, the paper analyses the occurrence of catastrophic shifts between different moving vegetation patterns. The study is conducted by numerical simulations of a system of partial differential equation which describes the dynamics of the biomass and water as a reaction-diffusion process. The model also includes the effect of self-toxicity produced by the biomass, which increases the capability of the system to self-organize in the space and time. The analysis reveals the existence of a variety of different periodic patterns moving in the space, like travelling waves and/ or pulse-like backfiring solutions. The precipitation rate is considered as system parameter and its effect on the vegetation patterns evolutions is analysed.
