The asymmetric effects on the escape rates from the stable states x±in the bistable system are analyzed. The results indicate that the multiplicative noise and the additive noise always enhance the particle escap...The asymmetric effects on the escape rates from the stable states x±in the bistable system are analyzed. The results indicate that the multiplicative noise and the additive noise always enhance the particle escape from stable states x±of bistable.However,the asymmetric parameter r enhances the particle escape from stable state x_+,and holds back the particle escape from stable state x_-.展开更多
We present a dynamical model of two-dimensional polydisperse granular gases with fractal size distribution, in which the disks are subject to inelastic mutual collisions and driven by standard white noise. The inhomog...We present a dynamical model of two-dimensional polydisperse granular gases with fractal size distribution, in which the disks are subject to inelastic mutual collisions and driven by standard white noise. The inhomogeneity of the disk size distribution can be measured by a fractal dimension df. By Monte Carlo simulations, we have mainly investigated the effect of the inhomogeneity on the statistical properties of the system in the same inelasticity case. Some novel results are found that the average energy of the system decays exponentially with a tendency to achieve a stable asymptotic value, and the system finally reaches a nonequilibrium steady state after a long evolution time. Furthermore, the inhomogeneity has great influence on the steady-state statistical properties. With the increase of the fractal dimension df, the distributions of path lengths and free times between collisions deviate more obviously from expected theoretical forms for elastic spheres and have an overpopulation of short distances and time bins. The collision rate increases with df, but it is independent of time. Meanwhile, the velocity distribution deviates more strongly from the Gaussian one, but does not demonstrate any apparent universal behavior.展开更多
Using a simplified nonlinearly theoretical grassland ecosystem proposed by Zeng et al.,we study the sensitivity and nonlinear instability of the grassland ecosystem to finiteamplitude initial perturbations with the ap...Using a simplified nonlinearly theoretical grassland ecosystem proposed by Zeng et al.,we study the sensitivity and nonlinear instability of the grassland ecosystem to finiteamplitude initial perturbations with the approach of conditional nonlinear optimal perturbation (CNOP).The results show that the linearly stable grassland (desert or latent desert) states can turn to be nonlinearly unstable with finite amplitude initial perturbations.When the precipitation is between the two bifurcation points,a large enough finite amplitude initial perturbation can induce a transition between the grassland statethe desert state or the latent desert.展开更多
In this paper, we propose a new input-to-state stable (ISS) synchronization method for chaotic behavior in nonlinear Bloch equations with external disturbance. Based on Lyapunov theory and linear matrix inequality ...In this paper, we propose a new input-to-state stable (ISS) synchronization method for chaotic behavior in nonlinear Bloch equations with external disturbance. Based on Lyapunov theory and linear matrix inequality (LMI) approach, for the first time, the ISS synchronization controller is presented to not only guarantee the asymptotic synchronization but also achieve the bounded synchronization error for any bounded disturbance. The proposed controller can be obtained by solving a convex optimization problem represented by the LMI. Simulation study is presented to demonstrate the effectiveness of the proposed synchronization scheme.展开更多
To reduce the fragility encountered in controller implementation, which is a measure of extent to describe small perturbations in controller parameters caused by rounding-off errors or component tolerances, and keep t...To reduce the fragility encountered in controller implementation, which is a measure of extent to describe small perturbations in controller parameters caused by rounding-off errors or component tolerances, and keep the system stability and performance, approaches of weighted eigenvalue sensitivity and stability radii comparison were used for computation and reduction of controller fragility. An algorithm has been derived for the efficient reduction of controller fragility, which used eigenstructure decomposition to obtain the suboptimal solution. The algorithm was tested for different control problems through reducing their fragility by a large margin. Different canonical forms were analyzed for fragility, including controllable canonical form, observable canonical form, modal canonical form, balanced realization and optimal (non-fragile) form. Different realizations were implemented through C language Matlab EXecutable (CMEX) S-function discrete state space block. Double precision calculations were performed. Open and closed loop controller realizations were compared with simulink state space (optimal) block. Results of comparison indicate that the optimal non-fragile controller realization shows better results both in open loop and closed loop realization.展开更多
The authors study a diffusive prey-predator model subject to the homogeneous Neumann boundary condition and give some qualitative descriptions of solutions to this reaction-diffusion system and its corresponding stead...The authors study a diffusive prey-predator model subject to the homogeneous Neumann boundary condition and give some qualitative descriptions of solutions to this reaction-diffusion system and its corresponding steady-state problem. The local and global stability of the positive constant steady-state are discussed, and then some results for non- existence of positive non-constant steady-states are derived.展开更多
基金Supported by the Natural Science Foundation of China under Grant No.10865006the Natural Science Foundation of Shaanxi Province under Grant No.2010JQ1014the Science Foundation of Baoji University of Science and Arts of China under Grant No.ZK0954
文摘The asymmetric effects on the escape rates from the stable states x±in the bistable system are analyzed. The results indicate that the multiplicative noise and the additive noise always enhance the particle escape from stable states x±of bistable.However,the asymmetric parameter r enhances the particle escape from stable state x_+,and holds back the particle escape from stable state x_-.
基金The project supported by National Natural Science Foundation of China under Grant No.10675048the Natural Science Foundation of Education Department of Hubei Province of China under Grant Nos.D200628002 and kz0627
文摘We present a dynamical model of two-dimensional polydisperse granular gases with fractal size distribution, in which the disks are subject to inelastic mutual collisions and driven by standard white noise. The inhomogeneity of the disk size distribution can be measured by a fractal dimension df. By Monte Carlo simulations, we have mainly investigated the effect of the inhomogeneity on the statistical properties of the system in the same inelasticity case. Some novel results are found that the average energy of the system decays exponentially with a tendency to achieve a stable asymptotic value, and the system finally reaches a nonequilibrium steady state after a long evolution time. Furthermore, the inhomogeneity has great influence on the steady-state statistical properties. With the increase of the fractal dimension df, the distributions of path lengths and free times between collisions deviate more obviously from expected theoretical forms for elastic spheres and have an overpopulation of short distances and time bins. The collision rate increases with df, but it is independent of time. Meanwhile, the velocity distribution deviates more strongly from the Gaussian one, but does not demonstrate any apparent universal behavior.
基金Supported by the NSF of Chian(4080502010702050+1 种基金60704015) Supported by the Natural Science Foundation of Henan Education Department(2010A100003)
文摘Using a simplified nonlinearly theoretical grassland ecosystem proposed by Zeng et al.,we study the sensitivity and nonlinear instability of the grassland ecosystem to finiteamplitude initial perturbations with the approach of conditional nonlinear optimal perturbation (CNOP).The results show that the linearly stable grassland (desert or latent desert) states can turn to be nonlinearly unstable with finite amplitude initial perturbations.When the precipitation is between the two bifurcation points,a large enough finite amplitude initial perturbation can induce a transition between the grassland statethe desert state or the latent desert.
文摘In this paper, we propose a new input-to-state stable (ISS) synchronization method for chaotic behavior in nonlinear Bloch equations with external disturbance. Based on Lyapunov theory and linear matrix inequality (LMI) approach, for the first time, the ISS synchronization controller is presented to not only guarantee the asymptotic synchronization but also achieve the bounded synchronization error for any bounded disturbance. The proposed controller can be obtained by solving a convex optimization problem represented by the LMI. Simulation study is presented to demonstrate the effectiveness of the proposed synchronization scheme.
文摘To reduce the fragility encountered in controller implementation, which is a measure of extent to describe small perturbations in controller parameters caused by rounding-off errors or component tolerances, and keep the system stability and performance, approaches of weighted eigenvalue sensitivity and stability radii comparison were used for computation and reduction of controller fragility. An algorithm has been derived for the efficient reduction of controller fragility, which used eigenstructure decomposition to obtain the suboptimal solution. The algorithm was tested for different control problems through reducing their fragility by a large margin. Different canonical forms were analyzed for fragility, including controllable canonical form, observable canonical form, modal canonical form, balanced realization and optimal (non-fragile) form. Different realizations were implemented through C language Matlab EXecutable (CMEX) S-function discrete state space block. Double precision calculations were performed. Open and closed loop controller realizations were compared with simulink state space (optimal) block. Results of comparison indicate that the optimal non-fragile controller realization shows better results both in open loop and closed loop realization.
基金Project supported by the National Natural Science Foundation of China (Nos. 10801090, 10726016)
文摘The authors study a diffusive prey-predator model subject to the homogeneous Neumann boundary condition and give some qualitative descriptions of solutions to this reaction-diffusion system and its corresponding steady-state problem. The local and global stability of the positive constant steady-state are discussed, and then some results for non- existence of positive non-constant steady-states are derived.