The dynamical evolution theory of the isolated oasis system

Assume that an oasis and its surrounding desert consist of an isolated system without mass and energy exchange with the outer environment. The characteristics of oasis evolution have been explored under the condition of system energy conservation. The results show that oasis evolves with two equilibrium states. The first equilibrium suggests a stable expansive and an unstable degraded oasis whereas the second equilibrium indicates a stable shrink and an unstable increase of the oasis area. If one equilibrium state is unstable, the components of the isolated system (oasis and desert) would tend to be no energy exchange and they each reach to energy balance respectively. Oasis would maintain its initial area in this case. Further analyses point out that the two equilibrium states have completely different characteristics. In the first equilibrium state, a higher vegetation albedo, lower soil albedo and larger canopy resistance, and direr soil both contribute to the oasis area expansion, accompanying an excessive large desert soil and vegetation canopy temperature difference (SCTD). In the second equilibrium state, however, a lower vegetation albedo, higher soil albedo and small canopy resistance, and wetter soil benefit the oasis area to stay near its initial value, following a moderate SCTD. The convergent trajectories of the initial values in phase space are influenced by the separatrices of the equilibrium points. Higher temperature is an advantage factor for initial values convergent to the oasis expansion solution.