Application Of The Conditional Nonlinear Optimal Perturbations Method In Sensitivity Analysis Of The Grassland Desertification

The Grassland desertification has become the most serious problems in environment society and economy. In progress of grassland desertification is a very complex ecological community as all open nonlinear system in which a variety of complex physical, chemical and biological reactions occur is formed. In this paper, based on the dynamical model for desertification, a new approach of conditional nonlinear optimal perturbation (CNOP) is adopted to investigate the initial perturbations and parameters perturbations sensitivity of the grassland ecosystem. The numerical results:(1) The impact of the initial perturbations(vegetation) on the grassland ecosystem has been studied in this paper. For R less than the bifurcation point R1, DES is nonlinearly stable, it is indicted that if rainfall rate is insufficient, although vegetation is increased, the system will return to desert state after a period of time; when R is lager than the bifurcation point R2, GES is also nonlinearly stable, it is indicted that if rainfall rate is sufficient, vegetation is increased, but the system will return to vegetation state after a period of time; In case of R between R1and R2, the grassland system is fragile, a large enough initial finite-amplitude perturbation can induce a transition from DES(GES) to GES(DES).(2) The impact of the parameters perturbations(rainfall rate) on the grassland ecosystem has been studied in this paper, we only studied the vegetation state. In case of R between R1and R2,if the constraint condition of perturbation is lager than R-R1, the GES can return to DES after a period of time; when R is lager than the bifurcation point R2, the optimal parameters perturbations are positive numbers, so rainfall rate is sufficient, vegetation will increase, the system will not occur steady-state conversion.