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HYDROLOGIC MODELING USING MULTIVARIATE STATE SPACE RECONSTRUCTION
"... State space reconstruction is an important tool used by dynamicists for characterizing and modeling dynamic processes. State space reconstruction indicates that the behavior of a dynamic process can be reconstructed from time series (signals) that describe a process’s state at each point in time. Op ..."
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State space reconstruction is an important tool used by dynamicists for characterizing and modeling dynamic processes. State space reconstruction indicates that the behavior of a dynamic process can be reconstructed from time series (signals) that describe a process’s state at each point in time
State Space Reconstruction in the Prediction of Chaotic Time Series with Neural Nets
"... In the last years neural networks have been used to predict chaotic time series. The predictability of neural nets, as well as of any other prediction model, is limited over shorttime lengths due to the chaotic character of the scalar time series. Standard backpropagation neural networks are only u ..."
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used in this work. It is shown that the quality of the prediction is drastically dependent on the structure of the input layer rather than the rest of the architecture of the net. In terms of dynamical system theory, the input layer indicates the reconstruction of state space from the scalar time
State space reconstruction parameters in the analysis of chaotic time series  the role of the time window length
 Physica D, 95:13
, 1996
"... dimension The most common state space reconstruction method in the analysis of chaotic time series is the Method of Delays (MOD). Many techniques have been suggested to estimate the parameters of MOD, i.e. the time delay τ and the embedding dimension m. We discuss the applicability of these techniqu ..."
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Cited by 25 (3 self)
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dimension The most common state space reconstruction method in the analysis of chaotic time series is the Method of Delays (MOD). Many techniques have been suggested to estimate the parameters of MOD, i.e. the time delay τ and the embedding dimension m. We discuss the applicability
Reconstruction of the Dynamics of Noisy Multivariate Time Series
"... We generalize the multi step prediction cost function for an unbiased reconstruction of the dynamics for noisy time series recently proposed for the case of scalar time series (which requires a reconstruction in delay space) to the case of multivariate time series data. PACS: 05.45.+b Key Words: Mul ..."
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We generalize the multi step prediction cost function for an unbiased reconstruction of the dynamics for noisy time series recently proposed for the case of scalar time series (which requires a reconstruction in delay space) to the case of multivariate time series data. PACS: 05.45.+b Key Words
Chaotic time series Part I: Estimation of some invariant properties in state space
 Modeling, Identification and Control, 15(4):205  224
, 1995
"... Certain deterministic nonlinear systems may show chaotic behaviour. Time series derived from such systems seem stochastic when analyzed with linear techniques. However, uncovering the deterministic structure is important because it allows constructing more realistic and better models and thus impro ..."
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Cited by 10 (5 self)
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improved predictive capabilities. This paper provides a review of two main key features of chaotic systems, the dimensions of their strange attractors and the Lyapunov exponents. The emphasis is on state space reconstruction techniques that are used to estimate these properties, given scalar observations
Dynamic Reconstruction of a Chaotic Process: Stability Considerations
, 1998
"... In this paper we address some fundamental issues pertaining to the dynamic reconstruction of a chaotic process, given an observable time series of the process. The issues considered are (1) the stability of an iterated prediction system built around a predictive model, and (2) the accuracy of dynami ..."
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Cited by 2 (1 self)
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motivation of dynamic reconstruction is to make physical sense from an experimental time series without knowledge of the underlying physics of the problem. To be specific, consider an unknown dynamical system whose evolution (measured in discrete time) is described by the statespace model: (1) (2) where x
On StateSpace Reconstruction of the Dynamics of Microcantilever Interactions
"... In the process of analysis and reconstruction of the statespace of timeseries of a nonlinear dynamical system exhibiting chaotic behavior, it has been observed that when filtering chaotic time series using a linear Infinite Impulse Response filter, the Lyapunov dimension can become dependent on the ..."
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In the process of analysis and reconstruction of the statespace of timeseries of a nonlinear dynamical system exhibiting chaotic behavior, it has been observed that when filtering chaotic time series using a linear Infinite Impulse Response filter, the Lyapunov dimension can become dependent
Time Series Prediction by Chaotic Modeling of Nonlinear Dynamical Systems
"... We use concepts from chaos theory in order to model nonlinear dynamical systems that exhibit deterministic behavior. Observed time series from such a system can be embedded into a higher dimensional phase space without the knowledge of an exact model of the underlying dynamics. Such an embedding war ..."
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Cited by 9 (1 self)
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We use concepts from chaos theory in order to model nonlinear dynamical systems that exhibit deterministic behavior. Observed time series from such a system can be embedded into a higher dimensional phase space without the knowledge of an exact model of the underlying dynamics. Such an embedding
Exploring the Neural State Space Learning from OneDimension Chaotic Time Series
"... Absrmct Because the chaotic system is initial chndition sensitive, it is difficult to decide a proper initial state for a recurrent neural network to model observed onedimension chaotic time series. In this paper, a recurrent neural network with feedback composed of internal state is introduced to ..."
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Absrmct Because the chaotic system is initial chndition sensitive, it is difficult to decide a proper initial state for a recurrent neural network to model observed onedimension chaotic time series. In this paper, a recurrent neural network with feedback composed of internal state is introduced
Results 1  10
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