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Results for “Nonlinear Dynamics”

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PubMed1994

Predictive control of nonlinear systems based on identification by backpropagation networks.

Using the property of universal approximation of multilayer perceptron neural network, a class of discrete nonlinear dynamical systems are modeled by a perceptron with two hidden layers. A backpropagation algorithm is then used to train the model to identify the nonlinear systems to a desired level of accuracy. Based on the identified model, a one-step-ahead predictive control scheme is proposed in which the future control inputs are obtained through some nonlinear optimization process. Making use of the online learning properties of neural networks, the predictive control scheme is further developed into an adaptive one which is robust to the incompleteness of identification. Simulation results show that this neural control scheme works well even for some very complicated nonlinear systems.

Mathematics↗

PubMed1997

SISO nonlinear system identification using a fuzzy-neural hybrid system.

This paper describes a fuzzy-neural hybrid system for the identification of nonlinear dynamic systems with unknown parameters. The proposed model takes the form of a context-sensitive module in which a fuzzy system is used as a function module and a multilayer neural network is used as a context module. Fuzzy-neural hybrid systems with a decomposed structure reduce complexity and thus accelerate the learning process. Also, the parameters of a fuzzy system have clear physical meanings, which makes it possible to incorporate a priori knowledge into the selection of initial parameter values and constraints among parameter values. Since hybrid systems correspond to networks, it is feasible to construct fast, parallel devices to implement these models for practical applications. The gradient descent method for the adjustment of parameters in hybrid systems is discussed. Simulations demonstrate that the hybrid identification models suggested here for SISO dynamic systems are quite effective.

Fuzzy Logic↗

PubMed1998

Stochastic feedback and the regulation of biological rhythms.

We propose a general approach to the question of how biological rhythms spontaneously self-regulate, based on the concept of "stochastic feedback". We illustrate this approach by considering at a coarse-grained level the neuroautonomic regulation of the heart rate. The model generates complex dynamics and successfully acounts for key characteristics of cardiac variability, including the l/f power spectrum, the functional form and scaling of the distribution of variations, and correlations in the Fourier phases indicating nonlinear dynamics.

Circadian Rhythm↗

PubMed1993

[Chaos and fractals. Are these of interest to medical science?].

Biological systems are governed by nonlinear dynamics and often appear to be random, because the available information, though accurate, is usually incomplete. It is important to be aware of the fact that nonlinear deterministic systems can behave unpredictably in the long term. Traditional reductionism is unable to provide an adequate understanding of such systems. A more global description and explanation of forms, features and functions is required. Chaos theory and fractal geometry are of value in this respect. This article is an introduction to this relatively new field of science and mathematics.

Fractals↗

PubMed1999

Modeling heart rate variability by stochastic feedback.

We consider the question of how the cardiac rhythm spontaneously self-regulates and propose a new mechanism as a possible answer. We model the neuroautonomic regulation of the heart rate as a stochastic feedback system and find that the model successfully accounts for key characteristics of cardiac variability, including the 1/f power spectrum, the functional form and scaling of the distribution of variations of the interbeat intervals, and the correlations in the Fourier phases which indicate nonlinear dynamics.

Heart↗

PubMed2003

Unstable attractors induce perpetual synchronization and desynchronization.

Common experience suggests that attracting invariant sets in nonlinear dynamical systems are generally stable. Contrary to this intuition, we present a dynamical system, a network of pulse-coupled oscillators, in which unstable attractors arise naturally. From random initial conditions, groups of synchronized oscillators (clusters) are formed that send pulses alternately, resulting in a periodic dynamics of the network. Under the influence of arbitrarily weak noise, this synchronization is followed by a desynchronization of clusters, a phenomenon induced by attractors that are unstable. Perpetual synchronization and desynchronization lead to a switching among attractors. This is explained by the geometrical fact, that these unstable attractors are surrounded by basins of attraction of other attractors, whereas the full measure of their own basin is located remote from the attractor. Unstable attractors do not only exist in these systems, but moreover dominate the dynamics for large networks and a wide range of parameters.

Models, Theoretical↗

PubMed1997

Chaotic dynamics of sea clutter.

The notion that a deterministic nonlinear dynamical system (with relatively few degrees of freedom) can display aperiodic behavior has a strong bearing on sea clutter characterization: random-looking sea clutter may be the outcome of a chaotic process. This new approach envisages deterministic rules for the underlying sea clutter dynamics, in contrast to the stochastic approach where sea clutter is viewed as a random process with a large number of degrees of freedom. In this paper, we demonstrate, convincingly for the first time, the chaotic dynamics of sea clutter. We say so on the basis of results obtained using radar data collected from a series of extensive and thorough experiments, which have been carried out with ground-truthed sea clutter data sets at three different sites. The study includes correlation dimension analysis (based on the maximum likelihood principle) and Lyapunov spectrum analysis. The Lyapunov (Kaplan-Yorke) dimension, which is a byproduct of Lyapunov spectrum analysis, shows that it is indeed a good estimator of the correlation dimension. The Lyapunov spectrum also reveals that sea clutter is produced by a coupled system of nonlinear differential equations of order five or six. (c) 1997 American Institute of Physics.

Journal Article↗

PubMed1993

Time series analysis of complex dynamics in physiology and medicine.

A variety of mathematical methods have been developed to characterize complex rhythms that are observed in physiological systems. These methods include classical techniques such as the mean, standard deviation, and power spectrum, as well as newer methods suggested by nonlinear dynamics including the dimension, Lyapunov number, and entropy. This paper reviews the various ways in which these measures have been applied to analyze physiological dynamics with emphasis on the potential advantages and pitfalls of the various approaches. We conclude that these methods may be useful to help characterize complex time series, but only rarely is it possible to use these methods to establish deterministic chaos in a given time series.

Animals↗

PubMed1999

Heart rate dynamics before spontaneous onset of ventricular fibrillation in patients with healed myocardial infarcts.

The traditional methods of analyzing heart rate (HR) variability have failed to predict imminent ventricular fibrillation (VF). We sought to determine whether new methods of analyzing RR interval variability based on nonlinear dynamics and fractal analysis may help to detect subtle abnormalities in RR interval behavior before the onset of life-threatening arrhythmias. RR interval dynamics were analyzed from 24-hour Holter recordings of 15 patients who experienced VF during electrocardiographic recording. Thirty patients without spontaneous or inducible arrhythmia events served as a control group in this retrospective case control study. Conventional time- and frequency-domain measurements, the short-term fractal scaling exponent (alpha) obtained by detrended fluctuation analysis, and the slope (beta) of the power-law regression line (log power - log frequency, 10(-4)-10(-2) Hz) of RR interval dynamics were determined. The short-term correlation exponent alpha of RR intervals (0.64 +/- 0.19 vs 1.05 +/- 0.12; p <0.001) and the power-law slope beta (-1.63 +/- 0.28 vs -1.31 +/- 0.20, p <0.001) were lower in the patients before the onset of VF than in the control patients, but the SD and the low-frequency spectral components of RR intervals did not differ between the groups. The short-term scaling exponent performed better than any other measurement of HR variability in differentiating between the patients with VF and controls. Altered fractal correlation properties of HR behavior precede the spontaneous onset of VF. Dynamic analysis methods of analyzing RR intervals may help to identify abnormalities in HR behavior before VF.

Aged↗

PubMed2000

Proper orthogonal decomposition and galerkin projection for a three-dimensional plasma dynamical system

A general method by which to investigate nonlinear dynamical systems close to a stability threshold is presented. This method combines a proper orthogonal decomposition and a subsequent Galerkin projection. This technique is applied to three-dimensional resistive ballooning plasma fluctuations in a tokamak. The corresponding dynamical system belongs to a large family of convective fluid systems including Rayleigh-Benard convection. A proper orthogonal decomposition of the fluctuating signal obtained by numerical simulation shows that the relevant modes are close to the linear (global) modes. The Galerkin projection provides a low-dimensional system that allows the study of shear flow generation, its subsequent fluctuation reduction, and the evolution to oscillating states.

Journal Article↗

PubMed2000

Self-exciting chaos as a dynamic model for irregular neural spiking

We introduce a nonlinear dynamical system with self-exciting chaotic dynamics. Its interspike interval return map shows a noisy Poisson-like distribution. Spike sequences from different initial conditions are unrelated but possess the same mean frequency. In the presence of noisy perturbations, sequences started from different initial conditions synchronize. The features of the model are compared with experimental results for irregular spike sequences in neurons. Self-exciting chaos offers a mechanism for temporal coding of complex input signals.

Journal Article↗

PubMed2002

Array-enhanced coherence resonance and forced dynamics in coupled FitzHugh-Nagumo neurons with noise.

Nonlinear dynamics of coupled FitzHugh-Nagumo neurons subject to independent noise is analyzed. A kind of self-sustained global oscillation with almost synchronous firing is generated by array-enhanced coherence resonance. Further, forced dynamics of the self-sustained global oscillation stimulated by sinusoidal input is analyzed and classified as synchronized, quasiperiodic, and chaotic responses just like the forced oscillations in nerve membranes observed by in vitro experiments with squid giant axons. Possible physiological importance of such forced oscillations is also discussed.

Animals↗

PubMed2005

Sensor fault diagnosis for nonlinear processes with parametric uncertainties.

This paper addresses the problem of detecting, discriminating, and reconstructing sensor faults for nonlinear systems with known model structure but uncertainty in the parameters of the process. The convenience of the proposed technique lies in the fact that historical operational data and/or a priori fault information is not required to achieve accurate fault reconstruction except for fixed, short intervals. The overall fault diagnosis algorithm is composed of a series of nonlinear estimators, which estimates parameter and a fault isolation and identification filter. Parameter estimation and fault reconstruction cannot be performed accurately since faults and parametric uncertainty interact with each other. Therefore, these two tasks are performed at different time scales, where the fault diagnosis takes place at a more frequent rate than the parameter estimation. It is shown that the fault can be reconstructed under some realistic assumptions and the performance of the proposed methodology is evaluated on a simulated chemical process exhibiting nonlinear dynamic behavior.

Algorithms↗

PubMed2000

Nonlinear EEG analysis and its potential role in epileptology.

Deterministic chaos offers a striking explanation for apparently irregular behavior of the brain that is evidenced in the EEG. Recent developments in the physical-mathematical framework of the theory of nonlinear dynamics (colloquially often termed chaos theory) provide new concepts and powerful algorithms to analyze such time series. Because of its high versatility, nonlinear time series analysis has already gone beyond the physical sciences and, at present, is being successfully applied in a variety of disciplines, including cardiology, neurology, psychiatry, and epileptology. However, it is well known that different influencing factors limit the use of nonlinear measures to characterize EEG dynamics in a strict sense. Nevertheless, when interpreted with care, relative estimates of, e.g., the correlation dimension or the Lyapunov exponents, can reliably characterize different states of normal and pathologic brain function. In epileptology, extraction of nonlinear measures from the intracranially recorded EEG promises to be important for clinical practice. In addition to an immense reduction of information content of long-lasting EEG recordings, previous studies have shown that these measures enable (a) localization of the primary epileptogenic area in different cerebral regions during the interictal state, (b) investigations of antiepileptic drug effects, (c) analyses of spatio-temporal interactions between the epileptogenic zone and other brain areas, and (d) detection of features predictive of imminent seizure activity. Nonlinear time series analysis provides new and supplementary information about the epileptogenic process and thus contributes to an improvement in presurgical evaluation.

Brain Mapping↗

PubMedDate not supplied

On the impact of episode sensitization on the course of recurrent affective disorders.

Sensitization of an organism by recurrent disease episodes is postulated as a key mechanism governing the progressive long-term course of affective disorders. The particular significance is that episode sensitization could underly the transition from externally triggered disease episodes to autonomous episode generation. Functionally, this transition might be explained by positive feedback between a disease episode and the activity state of an organism which includes the introduction of a memory trace for generated disease episodes. Here we consider the functional consequences of episode sensitization for the course of recurrent affective disorders. We use a computational approach and extend our previously introduced model for the course of affective disorders by a feedback mechanism for episode sensitization. Depending on sensitization timescale and amount, triggered episodes leave the model in a sustained sensitized state or induce autonomous disease progression. Runaway activation can end in saturation. Remarkably, however, over a broad parametric range the progression ends in intermediate states with fluctuating disease patterns. This behavior results from the model's nonlinear dynamics and represents a situation where the feedback intermittently changes between positive and negative directions. Our simulations strongly support episode sensitization as an important disease mechanism for affective disorders. From a nonlinear standpoint, this mechanism offers an explanation not only for autonomous disease progression but also for occurence and stability of irregular rapid-cycling disease states.

Feedback↗

PubMed1998

Usefulness of non-linear EEG analysis.

Spectral analysis methods are useful for the evaluation of EEG signals. Nevertheless, they refer only to the frequency domain and ignore any potentially interesting phase information. Analytical methods based upon the theory of nonlinear dynamics provides this and additional information. We used both methods to evaluate the EEG signals of volunteers performing two distinct mental arithmetic tasks. We extracted the power spectrum, the coherence and nonlinear parameters (dimension, the first Lyapunov exponent, the Kolmogorov entropy, the mutual dimension and the dimensions based upon spatial embedding of the original data as well as their surrogates). We found that 1) the spatial embedding dimension differed from that of the surrogates, indicating nonlinearity, 2) there were differences between the two arithmetic tasks, and 3) the spectral and nonlinear methods differ in terms of the information they provide. Our results indicate that nonlinear analysis methods can be useful despite the fact that they are still at an early stage of development.

Adult↗

PubMed1997

Estimation of the correlation dimension of heart rate using surrogate data techniques.

Researchers have recently applied nonlinear dynamical systems theory to physiological time series data. However, the direct implementation of the deterministic equations used to estimate the correlation dimension is problematic for physiological data. Importantly, the distinction between a nonlinear process and noise is particularly difficult for experimental data. One technique that has been developed to help with this distinction is the use of surrogate data. These data preserve many of the properties of the original time series but in fact are a randomization of the original data. Whereas in a sufficiently high embedding space the estimates of the correlation dimension of a nonlinear process will plateau, such estimates for a noise process will continue to rise with increases in the embedding dimension. In the present experiment two data sets were examined. Heart period time series were collected from a female subject during spontaneous breathing and breathing paced at 15 breaths per minute. Both data sets consisted of approximately 3000 interbeat intervals and embedding dimensions of m = 2 through m = 6 were examined. Results indicate that the correlation dimension estimate for the spontaneous breathing data reached a plateau around 4, whereas the surrogate data for this series showed no such plateau. For the paced breathing data, both the original and the surrogate data failed to show evidence of a plateau in the estimates of the correlation dimension. These results suggest that caution must be used in interpreting finite values of correlation dimension as evidence of a chaotic attractor in experimental data if no test for determinism is performed.

Female↗

PubMed1994

Nonlinear interpretation of respiratory sinus arrhythmia in anesthesia.

A non-parametric method is presented for modelling nonlinear dynamic mechanisms of respiratory sinus arrhythmia (RSA) in anesthesia caused by positive pressure ventilation. RR interval sequences are shown with Tsay's linearity test to contain both short-term and long-term nonlinear components, which cannot completely be modelled with optimal linear methods. The nonlinear approach is based on Wiener's theory for broad-band random input signal. The input-output model is formed for tracheal pressure and RR interval sequence. Second-order and third-order nonlinearities in RSA fluctuation are found and demonstrated.

Adult↗