The effects of stochastic perturbations and periodic excitations on the eutrophicated lake ecosystem are explored.Unlike the existing work in detecting early warning signals,this paper presents the most probable trans...The effects of stochastic perturbations and periodic excitations on the eutrophicated lake ecosystem are explored.Unlike the existing work in detecting early warning signals,this paper presents the most probable transition paths to characterize the regime shifts.The most probable transition paths are obtained by minimizing the Freidlin-Wentzell(FW)action functional and Onsager-Machlup(OM)action functional,respectively.The most probable path shows the movement trend of the lake eutrophication system under noise excitation,and describes the global transition behavior of the system.Under the excitation of Gaussian noise,the results show that the stability of the eutrophic state and the oligotrophic state has different results from two perspectives of potential well and the most probable transition paths.Under the excitation of Gaussian white noise and periodic force,we find that the transition occurs near the nearest distance between the stable periodic solution and the unstable periodic solution.展开更多
The solutions of the following bilinear stochastic differential equation are studied [GRAPHICS] where A(t)(k), B-t are (deterministic) continuous matrix-valued functions of t and w(1) (t),..., w(m) (t) are m independe...The solutions of the following bilinear stochastic differential equation are studied [GRAPHICS] where A(t)(k), B-t are (deterministic) continuous matrix-valued functions of t and w(1) (t),..., w(m) (t) are m independent standard Brownian motions. Conditions are given such that the solution is positive if the initial condition is positive. The equation the most probable path must satisfy is also derived and applied to a mathematical finance problem.展开更多
We introduce the path length probability density function(PPDF) method, which is based on an equivalence theorem and parameterizes the aerosol scattering effect by adding four factors to the atmospheric transmittance ...We introduce the path length probability density function(PPDF) method, which is based on an equivalence theorem and parameterizes the aerosol scattering effect by adding four factors to the atmospheric transmittance model. Using simulated observations in the O2-A band, we examined the utility of the PPDF-based method to account for the aerosol scattering effect. First, observations were simulated using a forward model under different aerosol conditions; PPDF factors were then retrieved using an optimal estimation method; PPDF factors were used to reconstruct the observations; and finally, simulated true observations and reconstructions were compared. Analysis of the difference between the true observations and reconstructions confirmed the utility of the PPDF-based method. Additionally, the O2 band was demonstrated to be an efficient observing band for assisting the remote sensing of atmospheric trace gases in the near-infrared band.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.12072261 and 11872305)。
文摘The effects of stochastic perturbations and periodic excitations on the eutrophicated lake ecosystem are explored.Unlike the existing work in detecting early warning signals,this paper presents the most probable transition paths to characterize the regime shifts.The most probable transition paths are obtained by minimizing the Freidlin-Wentzell(FW)action functional and Onsager-Machlup(OM)action functional,respectively.The most probable path shows the movement trend of the lake eutrophication system under noise excitation,and describes the global transition behavior of the system.Under the excitation of Gaussian noise,the results show that the stability of the eutrophic state and the oligotrophic state has different results from two perspectives of potential well and the most probable transition paths.Under the excitation of Gaussian white noise and periodic force,we find that the transition occurs near the nearest distance between the stable periodic solution and the unstable periodic solution.
基金the General Research Fund of the University of Kansas.
文摘The solutions of the following bilinear stochastic differential equation are studied [GRAPHICS] where A(t)(k), B-t are (deterministic) continuous matrix-valued functions of t and w(1) (t),..., w(m) (t) are m independent standard Brownian motions. Conditions are given such that the solution is positive if the initial condition is positive. The equation the most probable path must satisfy is also derived and applied to a mathematical finance problem.
基金supported by the Key Program of the National Natural Science Foundation of China(Grant No.41130528)
文摘We introduce the path length probability density function(PPDF) method, which is based on an equivalence theorem and parameterizes the aerosol scattering effect by adding four factors to the atmospheric transmittance model. Using simulated observations in the O2-A band, we examined the utility of the PPDF-based method to account for the aerosol scattering effect. First, observations were simulated using a forward model under different aerosol conditions; PPDF factors were then retrieved using an optimal estimation method; PPDF factors were used to reconstruct the observations; and finally, simulated true observations and reconstructions were compared. Analysis of the difference between the true observations and reconstructions confirmed the utility of the PPDF-based method. Additionally, the O2 band was demonstrated to be an efficient observing band for assisting the remote sensing of atmospheric trace gases in the near-infrared band.
