The local chaos characteristics of the time series pressure fluctuations of gas liquid two phase flow in a self aspirated reversed flow jet loop reactor are studied by the deterministic chaos analysis technique. It...The local chaos characteristics of the time series pressure fluctuations of gas liquid two phase flow in a self aspirated reversed flow jet loop reactor are studied by the deterministic chaos analysis technique. It is found that the estimated local largest Lyapunov exponent is positive in all cases and the profile is similar to that of the local fractal dimension in this reactor. The positive largest Lyapunov exponent shows that the reactor is a nonlinear chaotic system. The obvious distribution indicates that the local nonlinear characteristic parameters such as the Lyapunov exponent and the fractal dimension could be applied to further study the flow characteristics such as the flow regine transitions and flow structures of the multi phase reactors.展开更多
An approach for short-term forecasting of municipal water consumption was presented based on the largest Lyapunov exponent of chaos theory. The chaotic characteristics of time series of urban water consumption were ex...An approach for short-term forecasting of municipal water consumption was presented based on the largest Lyapunov exponent of chaos theory. The chaotic characteristics of time series of urban water consumption were examined by means of the largest Lyapunov exponent and correlation dimension. By using the largest Lyapunov exponent a short-term forecasting model for urban water consumption was developed, which was compared with the artificial neural network (ANN) approach in a case study. The result indicates that the model based on the largest Lyapunov exponent has higher prediction precision and forecasting stability than the ANN method, and its forecasting mean relative error is 9.6% within its maximum predictable time scale while it is 60.6% beyond the scale.展开更多
Parametric resonance can lead to dangerously large rolling motions, endangering the ship, cargo and crew. The QR-faetorization method for calculating （LCEs） Lyapunov Characteristic Exponents was introduced; parametr...Parametric resonance can lead to dangerously large rolling motions, endangering the ship, cargo and crew. The QR-faetorization method for calculating （LCEs） Lyapunov Characteristic Exponents was introduced; parametric resonance stability of ships in longitudinal waves was then analyzed using LCEs. Then the safe and unsafe regions of target ships were then identified. The results showed that this method can be used to analyze ship stability and to accurately identify safe and unsafe operating conditions for a ship in longitudinal waves.展开更多
We report some new results associated with the synchronization behavior of two coupled double-well Duffing oscillators （DDOs）. Some sufficient algebraic criteria for global chaos synchronization of the drive and res...We report some new results associated with the synchronization behavior of two coupled double-well Duffing oscillators （DDOs）. Some sufficient algebraic criteria for global chaos synchronization of the drive and response DDOs via linear state error feedback control are obtained by means of Lyapunov stability theory. The synchronization is achieved through a bistable state in which a periodic attractor co-exists with a chaotic attractor. Using the linear perturbation analysis, the prevalence of attractors in parameter space and the associated bifurcations are examined. Subcritical and supercritical Hopf bifurcations and abundance of Arnold tongues -- a signature of mode locking phenomenon are found.展开更多
In this paper, explicit closed form expressions of nonsmooth strict Lyapunov tunctlons for impulsive hybrid time-varying systems with discontinuous right-hand side is provided. Lyapunov functions are expressed in term...In this paper, explicit closed form expressions of nonsmooth strict Lyapunov tunctlons for impulsive hybrid time-varying systems with discontinuous right-hand side is provided. Lyapunov functions are expressed in terms of known nonstrict Lyapunov functions for the dynamics and finite sums of persistency of excitation parameters.展开更多
文摘The local chaos characteristics of the time series pressure fluctuations of gas liquid two phase flow in a self aspirated reversed flow jet loop reactor are studied by the deterministic chaos analysis technique. It is found that the estimated local largest Lyapunov exponent is positive in all cases and the profile is similar to that of the local fractal dimension in this reactor. The positive largest Lyapunov exponent shows that the reactor is a nonlinear chaotic system. The obvious distribution indicates that the local nonlinear characteristic parameters such as the Lyapunov exponent and the fractal dimension could be applied to further study the flow characteristics such as the flow regine transitions and flow structures of the multi phase reactors.
基金Supported by National Natural Science Foundation of China (No.50578108) .
文摘An approach for short-term forecasting of municipal water consumption was presented based on the largest Lyapunov exponent of chaos theory. The chaotic characteristics of time series of urban water consumption were examined by means of the largest Lyapunov exponent and correlation dimension. By using the largest Lyapunov exponent a short-term forecasting model for urban water consumption was developed, which was compared with the artificial neural network (ANN) approach in a case study. The result indicates that the model based on the largest Lyapunov exponent has higher prediction precision and forecasting stability than the ANN method, and its forecasting mean relative error is 9.6% within its maximum predictable time scale while it is 60.6% beyond the scale.
文摘Parametric resonance can lead to dangerously large rolling motions, endangering the ship, cargo and crew. The QR-faetorization method for calculating （LCEs） Lyapunov Characteristic Exponents was introduced; parametric resonance stability of ships in longitudinal waves was then analyzed using LCEs. Then the safe and unsafe regions of target ships were then identified. The results showed that this method can be used to analyze ship stability and to accurately identify safe and unsafe operating conditions for a ship in longitudinal waves.
基金supported by a fellowship of the Alexander von Humboldt Foundation in Bonn, Germanythe Royal Society of London, British Academy and Physical Sciences Research Council, UK, under the Newton International Fellowship scheme.
文摘We report some new results associated with the synchronization behavior of two coupled double-well Duffing oscillators （DDOs）. Some sufficient algebraic criteria for global chaos synchronization of the drive and response DDOs via linear state error feedback control are obtained by means of Lyapunov stability theory. The synchronization is achieved through a bistable state in which a periodic attractor co-exists with a chaotic attractor. Using the linear perturbation analysis, the prevalence of attractors in parameter space and the associated bifurcations are examined. Subcritical and supercritical Hopf bifurcations and abundance of Arnold tongues -- a signature of mode locking phenomenon are found.
文摘In this paper, explicit closed form expressions of nonsmooth strict Lyapunov tunctlons for impulsive hybrid time-varying systems with discontinuous right-hand side is provided. Lyapunov functions are expressed in terms of known nonstrict Lyapunov functions for the dynamics and finite sums of persistency of excitation parameters.
