The Sensitivity Analysis of a Lake Ecosystem with the Conditional Nonlinear Optimal Perturbation Method

Abstract EN

The instability and sensitivity of a lake ecosystem to the finite-amplitude perturbations related to the initial condition and the parameter correspondingly are studied.

The CNOP-I and CNOP-P methods are adopted to investigate this nonlinear system.

The numerical results with CNOP-I method show that the lake ecosystem can be nonlinearly unstable with finite-amplitude initial perturbations when the nutrient loading rate is between the two bifurcation points.

A large enough finite amplitude initial perturbation, that is, CNOP-I, can induce a transition from an oligotrophic (eutrophic) state to an eutrophic (oligotrophic) state.

With CNOP-P method, it is shown that the lake ecosystem can be transformed from an oligotrophic (eutrophic) state to an eutrophic (oligotrophic) state with a large enough finite amplitude parameter perturbation, that is, CNOP-P, no matter how large the nutrient loading rate is.