Parameter estimation using balanced synchronization

Synchronization between experimental observations and a dynamical model with undetermined parameters can assist in completing the specification of the model parameters. The quality of the synchronization, a cost function to be minimized, typically depends on the difference between the data time series and the model time series. If the coupling between the data and the model is too strong, this cost function is small for any data and any model, and the variation of the cost function with respect to the parameters of interest is too small to permit selection of a value of the parameters. If the coupling is too small, synchronization is lost. We introduce two methods for balancing the competing desires of a small cost function and the numerical ability to determine parameters accurately. One method of ‘balanced’ synchronization adds a requirement that the conditional Lyapunov exponent of the model system, conditioned on being driven by the data, remain negative but small. The other method allows the coupling to vary in time according to the error in synchronization. This second method succeeds because the data and the model exhibit generalized synchronization in the region where the parameters of the model are well determined.     

Parameter identification and synchronization of spatiotemporal chaos in an uncertain Gray-Scott system

The zero-asymptotic property of sliding variables in discrete systems is extended to a continuous one and applied to partial differential equations which describe spatiotemporal chaos. A method of chaos synchronization and parameter identification is proposed. The synchronization controllers and the parameter recognizers are designed. The uncertain Gray-Scott system is taken as an example to verify the effectiveness of the method. Simulation results show that the identification variables in the parameter recognizers may take the place of the unknown parameters in both target and response systems. Global synchronization of the two spatiotemporal chaotic systems with uncertain parameters may be realized quickly after controllers are added. Supported by the Natural Science Foundation of Liaoning Province, China (Grant No. 20052151) and the Innovative Team Program of Liaoning Educational Committee     

Detecting anomalous phase synchronization from time series

Modeling approaches are presented for detecting an anomalous route to phase synchronization from time series of two interacting nonlinear oscillators. The anomalous transition is characterized by an enlargement of the mean frequency difference between the oscillators with an initial increase in the coupling strength. Although such a structure is common in a large class of coupled nonisochronous oscillators, prediction of the anomalous transition is nontrivial for experimental systems, whose dynamical properties are unknown. Two approaches are examined; one is a phase equational modeling of coupled limit cycle oscillators and the other is a nonlinear predictive modeling of coupled chaotic oscillators. Application to prototypical models such as two interacting predator-prey systems in both limit cycle and chaotic regimes demonstrates the capability of detecting the anomalous structure from only a few sets of time series. Experimental data from two coupled Chua circuits shows its applicability to real experimental system.     

Detecting synchronizations in an asymmetric vocal fold model from time series data

A nonlinear modeling approach is presented for the reconstruction of the synchronization structure in an asymmetric two-mass model from time series data. The asymmetric two-mass model describes a variety of normal and pathological human voices associated with synchronous and desynchronous oscillations of the two asymmetric vocal folds. Our technique recovers the synchronization diagram, which yields the regimes of synchronization as well as desynchronization, which are dependent upon the asymmetry parameter and the subglottal pressure. This allows the prediction of the regime of pathological phonation associated with desynchronization of the vocal folds from a few sets of recorded time series. It is shown that the modeling is quite effective when the time series data are chaotic and if they are taken from a regime of desynchronization. We discuss the applicability of the present approach as a diagnostic tool for voice pathologies.     

基于差分进化算法的混沌时间序列预测模型参数组合优化

为了提高混沌时间序列预测模型的预测精度,提出一种基于差分进化（DE）算法的相空间重构和最小二乘支持向量机（LSSVM）模型参数组合优化方法．该方法将相空间重构参数和LSSVM预测模型参数进行组合作为差分进化算法的个体,以混沌时间序列预测精度作为个体的适应度函数,通过循环迭代获得最优参数组合．几个混沌时间序列的仿真实验结果表明,与传统的优化方法相比,参数组合优化方法具有更高的预测精度．     

Parameter estimation for the piecewice-polynomial mean value trend of a stochastic time series

We consider the problem of mean value trend estimation for a stochastic time series in a mixture with noise. The trend is simulated as a polynomial function of time with parameters changing discontinuously at a random instant. The proposed solution of this problem is based on the optimal nonlinear filtering theory for pulsed Markovian processes. An algorithm for approximate estimation of piesewise-linear trend parameters is devised as an example. The results of numerical simulation of a synthesized algorithm are presented. Lobachevsky State University, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 11, pp. 1405–1415, November, 1997.     

地块支持下MODIS-NDVI时间序列冬小麦种植面积测量研究

在大尺度冬小麦种植面积测量中,MODIS(moderate resolution imaging spectrometer)数据对绝大部分地区可实现全覆盖数据保障,具有很好的时间序列特征,在探测植物季相节律进行作物估产与动态监测上得到很好的应用,但因受到空间分辨率的限制,其测量结果的可靠性受到较大质疑.地块数据具有明确...     

Parameter estimation based synchronization for an epidemic model with application to tuberculosis in Cameroon

We propose a method based on synchronization to identify the parameters and to estimate the underlying variables for an epidemic model from real data. We suggest an adaptive synchronization method based on observer approach with an effective guidance parameter to update rule design only from real data. In order, to validate the identifiability and estimation results, numerical simulations of a tuberculosis (TB) model using real data of the region of Center in Cameroon are performed to estimate the parameters and variables. This study shows that some tools of synchronization of nonlinear systems can help to deal with the parameter and state estimation problem in the field of epidemiology. We exploit the close link between mathematical modelling, structural identifiability analysis, synchronization, and parameter estimation to obtain biological insights into the system modelled.     

Theoretical and experimental studies of parameter estimation based on chaos feedback synchronization

In this paper, we perform theoretical and experimental studies of parameter estimation based on chaos feedback synchronization. The Chua chaotic system is applied as the original system, and its time series of a single variable is applied as a feedback variable to drive a simulative system. The simplex method is employed to minimize the synchronization error in the simulative system to iteratively approach the original system parameters. Furthermore, the effects of feedback function, feedback weight, and noise are investigated. The parameter estimation method based on feedback synchronization shows its robustness to noise perturbation. Finally, the circuit experiment of parameter estimation is implemented in order to examine its practical applicability. The original Chua circuit parameters can be well approached from its recorded time series of a single variable. The results show the parameter estimation method based on feedback synchronization may be capable of estimating real system parameters from a chaotic time series.     

Multiparameter estimation using only a chaotic time series and its applications

An important extension to the techniques of synchronization-based parameter estimation is presented. Based on adaptive chaos synchronization, several methods are proposed to dynamically estimate multiple parameters using only a scalar chaotic time series. In comparison with previous schemes, the presented methods decrease the cost of parameter estimation and are more applicable in practice. Numerical examples are used to demonstrate the effectiveness and robustness of the presented methods. As an example application, an implementation of multichannel digital communication is proposed, where multiparameter modulation is used to simultaneously transmit more than one digital message. From a theoretical perspective, such an encoding increases the difficulty to directly read out the message from the transmitted signal and decreases the implementation cost.     

Parameter identification and synchronization of an uncertain Chen chaotic system via adaptive control

A systematic design process of adaptive synchronization and parameter identification of an uncertain Chen chaotic system is provided.With this new and effective method,parameter identification and synchronization of the Chen system,with all the system parameters unknown,can be achieved simultaneously.Theoretical proof and numerical simulation demonstrate the effectiveness and feasibility of the proposed method.     

Impact of modulated multiple optical feedback time delays on laser diode chaos synchronization

By studying laser diodes subject to multiple time-delayed optical feedback, we demonstrate that the signatures of time delays in the autocorrelation function of the laser output can be erased in systems incorporating modulated feedback time delays. This property enhances the suitability of such laser systems highly suitable for secure chaos-based communication systems. Chaos synchronization properties of a laser-based modulated multiple time-delayed system are also reported for the first time.     

The dynamics of exchange rate time series and the chaos game

This work presents a novel method of reconstructing some relevant characteristics of exchange rate time series by the superposition of two components: a mostly deterministic one, the chaos game as expressed by the Yuan/USD exchange rate and a purely stochastic one, Gaussian white noise. We analyzed 20 economic systems with the average Index of Economic Freedom above 50. The considered characteristics (the Lempel-Ziv complexity index, the slimness of the distribution and the Iterated Function Systems clumpiness test) are well reproduced by the reconstruction process. Additional confirmation is obtained by an analysis of the exchange rate of the Romanian national currency as an example of an application of the method to a transition economy, and by an analysis of the time series of the Euro-zone as an example of an application to a multinational system using a shorter time series.     

Parameter identification of chaos system based on unknown parameter observer

Parameter identification of chaos system based on unknown parameter observer is discussed generally. Based on the work of Guan et al. [X.P. Guan, H.P. Peng, L.X. Li, et al., Acta Phys. Sinica 50 (2001) 26], the design of unknown parameter observer is improved. The application of the improved approach is extended greatly. The works in some literatures [X.P. Guan, H.P. Peng, L.X. Li, et al., Acta Phys. Sinica 50 (2001) 26; J.H. Lü, S.C. Zhang, Phys. Lett. A 286 (2001) 148; X.Q. Wu, J.A. Lu, Chaos Solitons Fractals 18 (2003) 721; J. Liu, S.H. Chen, J. Xie, Chaos Solitons Fractals 19 (2004) 533] are only the special cases of our Corollaries 1 and 2. Some observers for Lü system and a new chaos system are designed to test our improved method, and simulations results demonstrate the effectiveness and feasibility of the improved approach.     

Mean first-passage time of an asymmetric bistable system driven by colour-correlated noise

In this paper, the effect of every parameter (including p, q, r, \la, \tau) on the mean first-passage time (MFPT) is investigated in an asymmetric bistable system driven by colour-correlated noise. The expression of MFPT has been obtained by applying the steepest-descent approximation. Numerical results show that (1) the intensity of multiplicative noise p and the intensity of additive noise q play different roles in the MFPT of the system, (2) suppression appears on the curve of the MFPT with small \la (e.g. \la<0.5) but there is a peak on the curve of the MFPT when \la is big (e.g. \la >0.5), and (3) with different values of r (e.g. r=0.1, 0.5, 1.5), the effort of \tau on the MFPT is diverse.     

Quantum chaos of an exciton-phonon system

A simple model of an exciton-phonon system is studied in connection with quantum chaos.     

On the estimation of persistence in geophysical time series

The estimation of persistence (or: self-correlation) is necessary to evaluate the effective degree of freedom (or: the number of statistically independent samples) of a geophysical time series. The application of textbook definitions may result in problems when the time series contains periodic signals. This is demonstrated with analytical solutions for a given auto-correlation function. On physical grounds, in this paper we estimate the persistence time as the integral over the absolute value of the auto-correlation function. This procedure has been proposed by Stratonovich and is shown to work for slow and fast oscillations involved. In the practical part of the paper, a 42-year long time series of phase height measurements at Kühlungsborn (54 ^∘N, 12 ^∘E) is studied. In the period band between 2.7 and 27 years, it shows a persistence time of about 12 years and an effective degree of freedom of 3.5. Hence, the negative trend of 310 meters per decade was found to be significant at a level of 86 %. This level could be raised if the time series were longer.     

Spatiotemporal chaos synchronization of an uncertain network based on sliding mode control

The sliding mode control method is used to study spatiotemporal chaos synchronization of an uncertain network.The method is extended from synchronization between two chaotic systems to the synchronization of complex network composed of N spatiotemporal chaotic systems.The sliding surface of the network and the control input are designed.Furthermore,the effectiveness of the method is analysed based on the stability theory.The Burgers equation with spatiotemporal chaos behavior is taken as an example to simulate the experiment.It is found that the synchronization performance of the network is very stable.