An ecosystem with a tipping in equilibrium state shows a bistability point with two equilibrium states for one set of conditions. In this case, changing the internal conditions and external perturbations can both cause the ecosystem to jump from one stable state to the other. Emerging desert landscapes is a consequences of non-linear responses of ecosystem to these outgoing environmental perturbations. These reactions are with resilience oscillations and equilibrium states alterations in an ecosystem. This paper presents chaotic behaviour of arid ecosystem over far from equilibrium where bifurcation points in stability route of ecosystem can represent a stable state of desert landscape over time. Adding one or more dimensions of periodicity to the ecosystem lead to a periodic orbit. In other word a path of stable equilibria is replaced by a periodic orbit which is a common behaviour in all of ecosystem with naturally periodic characteristics. This switch is called a Hopf bifurcation. This article shows that analysing ecosystem behaviour close to the tipping points (thresholds) can be a useful tool to predict desertification process. In this paper base on equilibria route concepts, has been explained desertification phenomenon over Hopf bifurcation and resilience oscillations in arid ecosystems. The results shows that less stable ecosystem indicated a higher amplitudes of fluctuation; conversely, a cessation of periodicity can signify a collapse in ecosystem which called desertification state.

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