This paper provides an overview of significant advances in nonlinear stochastic dynamics during the past two decades, including random response, stochastic stability, stochastic bifurcation, first passage problem and ...This paper provides an overview of significant advances in nonlinear stochastic dynamics during the past two decades, including random response, stochastic stability, stochastic bifurcation, first passage problem and nonlinear stochastic control. Topics for future research are also suggested.展开更多
With the integration of renewable power and electric vehicle,the power system stability is of increasing concern because the active power generated by the renewable energy and absorbed by the electric vehicle vary ran...With the integration of renewable power and electric vehicle,the power system stability is of increasing concern because the active power generated by the renewable energy and absorbed by the electric vehicle vary randomly.Based on the deterministic differential equation model,the nonlinear and linear stochastic differential equation models of power system under Gauss type random excitation are proposed in this paper.The angle curves under different random excitations were simulated using Euler-Maruyama(EM) numerical method.The numerical stability of EM method was proved.The mean stability and mean square stability of the power system under Gauss type of random small excitation were verified theoretically and illustrated with simulation sample.展开更多
This paper aims to perform a comparison of deterministic and stochastic models.The stochastic modelling is a more realistic way to study the dynamics of gonorrhoea infection as compared to its corresponding determinis...This paper aims to perform a comparison of deterministic and stochastic models.The stochastic modelling is a more realistic way to study the dynamics of gonorrhoea infection as compared to its corresponding deterministic model.Also,the deterministic solution is itself mean of the stochastic solution of the model.For numerical analysis,first,we developed some explicit stochastic methods,but unfortunately,they do not remain consistent in certain situations.Then we proposed an implicitly driven explicit method for stochastic heavy alcohol epidemic model.The proposed method is independent of the choice of parameters and behaves well in all scenarios.So,some theorems and simulations are presented in support of the article.展开更多
This is the second of two consecutive papers focusing on the filtering algorithm for a nonlinear stochastic discretetime system with linear system state equation. The first paper established a derivative unscented Kal...This is the second of two consecutive papers focusing on the filtering algorithm for a nonlinear stochastic discretetime system with linear system state equation. The first paper established a derivative unscented Kalman filter（DUKF） to eliminate the redundant computational load of the unscented Kalman filter（UKF） due to the use of unscented transformation（UT） in the prediction process. The present paper studies the error behavior of the DUKF using the boundedness property of stochastic processes. It is proved that the estimation error of the DUKF remains bounded if the system satisfies certain conditions. Furthermore, it is shown that the design of the measurement noise covariance matrix plays an important role in improvement of the algorithm stability. The DUKF can be significantly stabilized by adding small quantities to the measurement noise covariance matrix in the presence of large initial error. Simulation results demonstrate the effectiveness of the proposed technique.展开更多
基金The project supported by the National Natural Science Foundation of China (19972059)
文摘This paper provides an overview of significant advances in nonlinear stochastic dynamics during the past two decades, including random response, stochastic stability, stochastic bifurcation, first passage problem and nonlinear stochastic control. Topics for future research are also suggested.
基金supported by the National Natural Science Foundation of China (Grant Nos. 51137002,51190102)the Fundamental Research Funds for the Central Universities (Grant No. BZX/09B101-32)
文摘With the integration of renewable power and electric vehicle,the power system stability is of increasing concern because the active power generated by the renewable energy and absorbed by the electric vehicle vary randomly.Based on the deterministic differential equation model,the nonlinear and linear stochastic differential equation models of power system under Gauss type random excitation are proposed in this paper.The angle curves under different random excitations were simulated using Euler-Maruyama(EM) numerical method.The numerical stability of EM method was proved.The mean stability and mean square stability of the power system under Gauss type of random small excitation were verified theoretically and illustrated with simulation sample.
基金The first author also thanks Prince Sultan University for funding this work through research-group number RG-DES2017-01-17.
文摘This paper aims to perform a comparison of deterministic and stochastic models.The stochastic modelling is a more realistic way to study the dynamics of gonorrhoea infection as compared to its corresponding deterministic model.Also,the deterministic solution is itself mean of the stochastic solution of the model.For numerical analysis,first,we developed some explicit stochastic methods,but unfortunately,they do not remain consistent in certain situations.Then we proposed an implicitly driven explicit method for stochastic heavy alcohol epidemic model.The proposed method is independent of the choice of parameters and behaves well in all scenarios.So,some theorems and simulations are presented in support of the article.
基金supported by the National Natural Science Foundation of China(Grant No.61174193)the Doctorate Foundation of Northwestern Polytechnical University,China(Grant No.CX201409)
文摘This is the second of two consecutive papers focusing on the filtering algorithm for a nonlinear stochastic discretetime system with linear system state equation. The first paper established a derivative unscented Kalman filter（DUKF） to eliminate the redundant computational load of the unscented Kalman filter（UKF） due to the use of unscented transformation（UT） in the prediction process. The present paper studies the error behavior of the DUKF using the boundedness property of stochastic processes. It is proved that the estimation error of the DUKF remains bounded if the system satisfies certain conditions. Furthermore, it is shown that the design of the measurement noise covariance matrix plays an important role in improvement of the algorithm stability. The DUKF can be significantly stabilized by adding small quantities to the measurement noise covariance matrix in the presence of large initial error. Simulation results demonstrate the effectiveness of the proposed technique.
