A General Approach for Synchronization of Chaotic Systems with Parameters Perturbation

By making use of the theory of stability for dynamical systems, a general approach for synchronization of chaotic systems with parameters perturbation is presented, and a general method for determining control function is introduced. The Rossler system is employed to verify the effectiveness of the method, and the theoretical results are confirmed by simulations.

ON THE SINGULAR PERTURBATION OF A NONLINEAR ORDINARY DIFFERENTIAL EQUATION WITH TWO PARAMETERS

In this paper,the method of differential inequalities has been applied to study theboundary value problems of nonlinear ordinary differential equation with two parameters.The asymptotic solutions have been found and the remainders have been estimated.

Advances in experiments and numerical simulations on the effects of stress perturbations on fault slip

Laboratory experiments and numerical simulations on rock friction perturbations,an important means for understanding the mechanism and influencing factors of stress-triggered earthquakes,are of great significance for studying earthquake mechanisms and earthquake hazard analysis.We reviews the experiments and numerical simulations on the effects of stress perturbations on fault slip,and the results show that stress perturbations can change fault stress and trigger earthquakes.The Coulomb failure criterion can shed light on some questions about stress-triggering earthquakes but cannot explain the time dependence of earthquake triggering nor be used to investigate the effect of heterogeneous stress perturbations.The amplitude and period are important factors affecting the correlation between stress perturbation and fault instability.The effect of the perturbation period on fault instability is still controversial,and the effect of the high-frequency perturbation on earthquakes may be underestimated.Normal and shear stress perturbation can trigger fault instability,but their effects on fault slip differ.It is necessary to distinguish whether the stress perturbation is dominated by shear or normal stress change when it triggers fault instability.Fault tectonic stress plays a decisive effect on the mode of fault instability and earthquake magnitude.Acoustic emission activity can reflect the changes in fault stress and the progression of fault nucleation,and identify the meta-instability stage and precursor of fault instability,providing a reference for earthquake prediction.

Stabilization of spiral wave and turbulence in the excitable media using parameter perturbation scheme

This paper proposes a scheme of parameter perturbation to suppress the stable rotating spiral wave, meandering spiral wave and turbulence in the excitable media, which is described by the modified Fitzhug-Nagumo （MFHN） model. The controllable parameter in the MFHN model is perturbed with a weak pulse and the pulse period is decided by the rotating period of the spiral wave approximatively. It is confirmed that the spiral wave and spiral turbulence can be suppressed greatly. Drift and instability of spiral wave can be observed in the numerical simulation tests before the whole media become homogeneous finally.

Fuzzy finite difference method for heat conduction analysis with uncertain parameters

A new numerical technique named as fuzzy finite difference method is proposed to solve the heat conduction problems with fuzzy uncertainties in both the phys- ical parameters and initial/boundary conditions. In virtue of the level-cut method, the difference discrete equations with fuzzy parameters are equivalently transformed into groups of interval equations. New stability analysis theory suited to fuzzy difference schemes is developed. Based on the parameter perturbation method, the interval ranges of the uncertain temperature field can be approximately predicted. Subsequently, fuzzy solutions to the original difference equations are obtained by the fuzzy resolution theorem. Two numerical examples are given to demonstrate the feasibility and efficiency of the presented method for solving both steady-state and transient heat conduction problems.

Inducing Unstable Grassland Equilibrium States Due to Nonlinear Optimal Patterns of Initial and Parameter Perturbations:Theoretical Models

Due to uncertainties in initial conditions and parameters, the stability and uncertainty of grassland ecosystem simulations using ecosystem models are issues of concern. Our objective is to determine the types and patterns of initial and parameter perturbations that yield the greatest instability and uncertainty in simulated grassland ecosystems using theoretical models. We used a nonlinear optimization approach, i.e., a conditional nonlinear optimal perturbation related to initial and parameter perturbations （CNOP） approach, in our work. Numerical results indicated that the CNOP showed a special and nonlinear optimal pattern when the initial state variables and multiple parameters were considered simultaneously. A visibly different complex optimal pattern characterizing the CNOPs was obtained by choosing different combinations of initial state variables and multiple parameters in different physical processes. We propose that the grassland modeled ecosystem caused by the CNOP-type perturbation is unstable and exhibits two aspects： abrupt change and the time needed for the abrupt change from a grassland equilibrium state to a desert equilibrium state when the initial state variables and multiple parameters are considered simultaneously. We compared these findings with results affected by the CNOPs obtained by considering only uncertainties in initial state variables and in a single parameter. The numerical results imply that the nonlinear optimal pattern of initial perturbations and parameter perturbations, especially for more parameters or when special parameters are involved, plays a key role in determining stabilities and uncertainties associated with a simulated or predicted grassland ecosystem.

Ground-state energy of beryllium atom with parameter perturbation method

We present a perturbation study of the ground-state energy of the beryllium atom by incorporating double parameters in the atom＇s Hamiltonian. The eigenvalue of the Hamiltonian is then solved with a double-fold perturbation scheme,where the spin-spin interaction of electrons from different shells of the atom is also considered. Calculations show that the obtained ground-state energy is in satisfactory agreement with experiment. It is found that the Coulomb repulsion of the inner-shell electrons enhances the effective nuclear charge seen by the outer-shell electrons, and the shielding effect of the outer-shell electrons to the nucleus is also notable compared with that of the inner-shell electrons.

A filter algorithm for multi-measurement nonlinear system with parameter perturbation

An improved interacting multiple models particle filter (IMM-PF) algorithm is proposed for multi-measurement nonlinear system with parameter perturbation. It divides the perturbation region into sub-regions and assigns each of them a particle filter. Hence the perturbation problem is converted into a multi-model filters problem. It combines the multiple meas- urements into a fusion value according to their likelihood function. In the simulation study, we compared it with the IMM-KF and the H-infinite filter; the results testify to its advantage over the other two methods.

THE PARAMETER PERTURBATION METHOD ON ELASTIC WAVE EQUATION IN INHOMOGENEOUS MEDIUM

In this paper, the medium parameters of the elastic wave equation in inhomogeneous medium are rewritten by introducing the referential variables and the perturbational variables, and the wave equation whose sources are the medium parameter perturbational term in homogeneous medium is obtained. By using the Green function theory, the integral equation of the perturbational parameters is obtained. Then the displacement field in homogeneous medium is considered the result of the first iteration, and the displacement field is solved by this integral equation. When the perturbations of medium parameters are about 50 percent, this method can solve the displacement field effectively. from the analysis of the numerical results, the characteristics of wave field in inhomogeneous medium are obtained. The results conform with the local principles of wave function in inhomogeneous medium.

Application of H infinite control to ship steering system

Because the general object of ship steering control system is singular, the state Of rudder force and the state of disturbance are separated, and the generalized yaw output disturhance is obtained. Furthermore, singular system control problem of ship yaw and sway coupled system is transferred into nonsingular standard control problem. Then according to the linear fractional denoting algorithm of the rational function parameter perturbation system, the Linear Fractional Transform （LFT） model of yaw and sway coupled motion is solved, which is used to design the ship steering robust control system. For the ship steering system with the uncertain parameters, the robust control law is designed based on H^∞ μ-synthesis. And the robust performance of the system is analyzed and the simulation validation is made. Simulation results show that the designed control system has excellent control effect and robustness.

Response of a Grassland Ecosystem to Climate Change in a Theoretical Model

The response of a grassland ecosystem to climate change is discussed within the context of a theoretical model.An optimization approach,a conditional nonlinear optimal perturbation related to parameter（CNOP-P） approach,was employed in this study.The CNOP-P,a perturbation of moisture index in the theoretical model,represents a nonlinear climate perturbation.Two kinds of linear climate perturbations were also used to study the response of the grassland ecosystem to different types of climate changes.The results show that the extent of grassland ecosystem variation caused by the CNOP-P-type climate change is greater than that caused by the two linear types of climate change.In addition,the grassland ecosystem affected by the CNOP-P-type climate change evolved into a desert ecosystem,and the two linear types of climate changes failed within a specific amplitude range when the moisture index recovered to its reference state.Therefore,the grassland ecosystem response to climate change was nonlinear.This study yielded similar results for a desert ecosystem seeded with both living and wilted biomass litter.The quantitative analysis performed in this study also accounted for the role of soil moisture in the root zone and the shading effect of wilted biomass on the grassland ecosystem through nonlinear interactions between soil and vegetation.The results of this study imply that the CNOP-P approach is a potentially effective tool for assessing the impact of nonlinear climate change on grassland ecosystems.

ESO-based robust predictive control of lunar module with fuel sloshing dynamics

An extended-state-observer(ESO) based predictive control scheme is proposed for the autopilot of lunar landing.The slosh fuel masses exert forces and torques on the rigid body of lunar module(LM),such disturbances will dramatically undermine the stability of autopilot system.The fuel sloshing dynamics and uncertainties due to the time-varying parameters are considered as a generalized disturbance which is estimated by an ESO from the measured attitude signals and the control input signals.Then a continuous-time predictive controller driven by the estimated states and disturbances is designed to obtain the virtual control input,which is allocated to the real control actuators according to a deadband logic.The 6-DOF simulation results reveal the effectiveness of the proposed method when dealing with the fuel sloshing dynamics and parameter perturbations.

Synchronization of chaos using radial basis functions neural networks

The Radial Basis Functions Neural Network （RBFNN） is used to establish the model of a response system through the input and output data of the system. The synchronization between a drive system and the response system can be implemented by employing the RBFNN model and state feedback control. In this case, the exact mathematical model, which is the precondition for the conventional method, is unnecessary for implementing synchronization. The effect of the model error is investigated and a corresponding theorem is developed. The effect of the parameter perturbations and the measurement noise is investigated through simulations. The simulation results under different conditions show the effectiveness of the method.

Adaptive control of bifurcation and chaos in a time-delayed system

In this paper,the stabilization of a continuous time-delayed system is considered.To control the bifurcation and chaos in a time-delayed system,a parameter perturbation control and a hybrid control are proposed.Then,to ensure the asymptotic stability of the system in the presence of unexpected system parameter changes,the adaptive control idea is introduced,i.e.,the perturbation control parameter and the hybrid control parameter are automatically tuned according to the adaptation laws,respectively.The adaptation algorithms are constructed based on the Lyapunov-Krasovskii stability theorem.The adaptive parameter perturbation control and the adaptive hybrid control methods improve the corresponding constant control methods.They have the advantages of increased stability,adaptability to the changes of the system parameters,control cost saving,and simplicity.Numerical simulations for a well-known chaotic time-delayed system are performed to demonstrate the feasibility and superiority of the proposed control methods.A comparison of the two adaptive control methods is also made in an experimental study.

Ensemble Forecast for Tropical Cyclone Based on CNOP-P Method:A Case Study of WRF Model and Two Typhoons

In this paper,we set out to study the ensemble forecast for tropical cyclones.The case study is based on the Conditional Nonlinear Optimal Perturbation related to Parameter(CNOP-P)method and the WRF model to improve the prediction accuracy for track and intensity,and two different typhoons are selected as cases for analysis.We first select perturbed parameters in the YSU and WSM6 schemes,and then solve CNOP-Ps with simulated annealing algorithm for single parameters as well as the combination of multiple parameters.Finally,perturbations are imposed on default parameter values to generate the ensemble members.The whole proposed procedures are referred to as the PerturbedParameter Ensemble(PPE).We also conduct two experiments,which are control forecast and ensemble forecast,termed Ctrl and perturbed-physics ensemble(PPhyE)respectively,to demonstrate the performance for contrast.In the article,we compare the effects of three experiments on tropical cyclones in aspects of track and intensity,respectively.For track,the prediction errors of PPE are smaller.The ensemble mean of PPE filters the unpredictable situation and retains the reasonably predictable components of the ensemble members.As for intensity,ensemble mean values of the central minimum sea-level pressure and the central maximum wind speed are closer to CMA data during most of the simulation time.The predicted values of the PPE ensemble members included the intensity of CMA data when the typhoon made landfall.The PPE also shows uncertainty in the forecast.Moreover,we also analyze the track and intensity from physical variable fields of PPE.Experiment results show PPE outperforms the other two benchmarks in track and intensity prediction.

On the Fifth-Order Stokes Solution for Steady Water Waves

This paper presents a universal fifth-order Stokes solution for steady water waves on the basis of potential theory. It uses a global perturbation parameter, considers a depth uniform current, and thus admits the flexibilities on the definition of the perturbation parameter and on the determination of the wave celerity. The universal solution can be extended to that of Chappelear （1961）, confirming the correctness for the universal theory. Furthermore, a particular fifth-order solution is obtained where the wave steepness is used as the perturbation parameter. The applicable range of this solution in shallow depth is analyzed. Comparisons with the Fourier approximated results and with the experimental measurements show that the solution is fairly suited to waves with the Ursell number not exceeding 46.7.

Impacts of parameter uncertainties on deep chlorophyll maximum simulation revealed by the CNOP-P approach

Parameter uncertainty is a primary source of uncertainty in ocean ecosystem simulations.The deep chlorophyll maximum(DCM)is a ubiquitous ecological phenomenon in the ocean.Using a theoretical nutrients-phytoplankton model and the conditional nonlinear optimal perturbation approach related to parameters,we investigated the eff ects of parameter uncertainties on DCM simulations.First,the sensitivity of single parameter was analyzed.The sensitivity ranking of 10 parameters was obtained by analyzing the top four specifi cally.The most sensitive parameter(background turbidity)aff ects the light supply for DCM formation,whereas the other three parameters(nutrient content of phytoplankton,nutrient recycling coeffi cient,and vertical turbulent diff usivity)control nutrient supply.To explore the interactions among diff erent parameters,the sensitivity of multiple parameters was further studied by examining combinations of four parameters.The results show that background turbidity is replaced by the phytoplankton loss rate in the optimal parameter combination.In addition,we found that interactions among these parameters are responsible for such diff erences.Finally,we found that reducing the uncertainties of sensitive parameters could improve DCM simulations remarkably.Compared with the sensitive parameters identifi ed in the single parameter analysis,reducing parameter uncertainties in the optimal combination produced better model performance.This study shows the importance of nonlinear interactions among various parameters in identifying sensitive parameters.In the future,the conditional nonlinear optimal perturbation approach related to parameters,especially optimal parameter combinations,is expected to greatly improve DCM simulations in complex ecosystem models.

Algorithm for Computation of Unstructured Real Stability Radius and Its Applications

An algorithm for the computation of the unstructured real stability radius of high dimensional linearsystem is presented. Using the accurate formula of the real stability radius of 2-dimensional system linear systemchecks the algorithm. The result shows that the algorithm is reliable and efficient. As applications, the unstructuredreal stability radii of 2-dimensional Chua's circuit and 3-dimensional piecewise-linear system are calculated, thedynamical orbits of the corresponding perturbed systems are simulated.

Mixed H_2/H_∞ Control Using a Fuzzy Singularly Perturbed Model with Multiple Perturbation Parameters for Gust Load Alleviation

This paper presents a mixed H21H∞ control using fuzzy singularly perturbed model （FSPM） with multiple perturbation parameters. Since FSPM with multiple perturbation parameters is an extension of models with a single perturbation parameter, the theoretical results are applicable to a larger class of systems described by multiple time scale nonlinear models, such as flying aircraft and flexible space robots. The parameter-independent solution of the mixed H21H∞ controller was obtained in the form of linear matrix inequalities （LMIs）. The application of this approach to gust load alleviation of a flying vehicle verifies its effectiveness and flexibility.

A Stochastic Extension of Macroscopic Stability Criterion of Nonequilibrium Steady State in Chemical Reaction Systems Governed by Master Equation

By means of both the separation of the perturbation in accordance with characteristic parnmeters and the Kramers Moyal-expansion of the master equation, it is shown that the time derivative of the partial excess quantity of stochastic entropy due to the deviation from the most probable path is related to the responsibility of a system to the external macroscopic perturbations. This evolution rate of the partial excess stochastic entropy is equivalent to the partlal excess stochastic entropy production, as well as the stochastic excess entropy production rate based on the stochastic potential npproach. It appears also as an eqivalent quantity of the Gibbs excess entropy production for the Polsson distribution. The macroscopic stability of chemical reaction systems is dominnted by this new stochastic quantity when the local equilibrium thermodynamics is broken down .