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Controlling chemical turbulence by global delayed feedback: pattern formation in catalytic CO oxidation on Pt(110).

Control of spatiotemporal chaos is one of the central problems of nonlinear dynamics. We report on suppression of chemical turbulence by global delayed feedback using, as an example, catalytic carbon monoxide oxidation on a platinum (110) single-crystal surface and carbon monoxide partial pressure as the controlled feedback variable. When feedback intensity was increased, spiral-wave turbulence was transformed into new intermittent chaotic regimes with cascades of reproducing and annihilating local structures on the background of uniform oscillations. The global feedback further led to the development of cluster patterns and standing waves and to the stabilization of uniform oscillations. These findings are reproduced by theoretical simulations.

Journal Article↗

Spatiotemporal self-organization in a surface reaction: from the atomic to the mesoscopic scale.

Scanning tunneling microscopy data revealed the atomic processes in propagating reaction fronts that occur in the catalytic oxidation of hydrogen on Pt(111). The fronts were also characterized on mesoscopic length scales with respect to their velocity and width. Simulations on the basis of a reaction-diffusion model reproduce the experimental findings qualitatively well. The quantitative comparison reveals the limitations of this traditional approach to modeling spatiotemporal pattern formation in nonlinear dynamics.

Journal Article↗

White-noise analysis of a neuron chain: an application of the Wiener theory.

The Wiener theory of nonlinear system identification was applied to a three-stage neuron chain in the catfish retina in order to determine the functional relationship between the artificial polarization of the horizontal cell membrane potential and the resulting discharge of the ganglion cell. A mathematical model was obtained that can predict quantitatively, with reasonable accuracy, the nonlinear, dynamic behavior of the neuron chain. The applicability of the method is discussed. We conclude that this is a very powerful method in the analysis of information transfer in the central nervous system.

Action Potentials↗

A constrained neural network Kalman filter for price estimation in high frequency financial data.

In this paper we present a neural network extended Kalman filter for modeling noisy financial time series. The neural network is employed to estimate the nonlinear dynamics of the extended Kalman filter. Conditions for the neural network weight matrix are provided to guarantee the stability of the filter. The extended Kalman filter presented is designed to filter three types of noise commonly observed in financial data: process noise, measurement noise, and arrival noise. The erratic arrival of data (arrival noise) results in the neural network predictions being iterated into the future. Constraining the neural network to have a fixed point at the origin produces better iterated predictions and more stable results. The performance of constrained and unconstrained neural networks within the extended Kalman filter is demonstrated on "Quote" tick data from the $/DM exchange rate (1993-1995).

Algorithms↗

Nonlinear system identification using a neo fuzzy neuron algorithm: electrical drive application.

This work presents a Neo-Fuzzy-Neuron algorithm for the identification of nonlinear dynamic systems at the point of view of a rotor flux observer. The algorithm training is on-line, has low computational cost, does not require previous training and its convergence in one step is proved. The gradient descent method is used for its weights adjustment. Simulation and experimental results demonstrate the effectiveness of the algorithm for flux observer of induction motor drive system.

Algorithms↗

Group performance and decision making.

Theory and research on small group performance and decision making is reviewed. Recent trends in group performance research have found that process gains as well as losses are possible, and both are frequently explained by situational and procedural contexts that differentially affect motivation and resource coordination. Research has continued on classic topics (e.g., brainstorming, group goal setting, stress, and group performance) and relatively new areas (e.g., collective induction). Group decision making research has focused on preference combination for continuous response distributions and group information processing. New approaches (e.g., group-level signal detection) and traditional topics (e.g., groupthink) are discussed. New directions, such as nonlinear dynamic systems, evolutionary adaptation, and technological advances, should keep small group research vigorous well into the future.

Cognition↗

Ca2+ excitability of the ER membrane: an explanation for IP3-induced Ca2+ oscillations.

Recent research dealing with experiments and theoretical models of Ca2+ excitability of the endoplasmic reticulum (ER) membrane induced by inositol 1,4,5-trisphosphate (IP3) is reviewed. Ca2+ excitability refers to the ability of a small increment of cytoplasmic Ca2+ concentration ([Ca2+]i) to trigger a large [Ca2+]i pulse or oscillations. Such nonlinear regenerative behavior is conferred by the existence of IP3 channels and Ca(2+)-ATPase transporters on the ER membrane, which extends throughout the cytoplasm. Ca2+ excitability resembles the plasma membrane electrical excitability of neurons and other cells: it is driven by the ionic concentration gradient across the ER membrane (higher Ca2+ concentration inside the ER); each [Ca2+]i spike partially consumes the prestored energy that is reestablished through ATP-dependent active transport; and [Ca2+]i, the excitation variable, controls the nonlinear dynamic release rate of ER Ca2+. This review focuses on the kinetic models based on these features and on experiments dealing with the kinetic properties of [Ca2+]i-dependent gating of the IP3 receptor channel. We summarize evidence in favor of two roles for [Ca2+]i in gating the channel's opening: activation at a rapid time scale and inactivation on a slower time scale. Exploiting an analogy to the well-known Hodgkin-Huxley model for neuronal electrical excitability, we show how Ca2+ excitability of the ER membrane can be explained by these gating properties combined with the ER Ca2+ pump activity. The theory's ability to predict is illustrated by comparing calculated with experimental [Ca2+]i responses for pituitary gonadotrophs under various stimulus conditions.

Animals↗

A point-process model of human heartbeat intervals: new definitions of heart rate and heart rate variability.

Heart rate is a vital sign, whereas heart rate variability is an important quantitative measure of cardiovascular regulation by the autonomic nervous system. Although the design of algorithms to compute heart rate and assess heart rate variability is an active area of research, none of the approaches considers the natural point-process structure of human heartbeats, and none gives instantaneous estimates of heart rate variability. We model the stochastic structure of heartbeat intervals as a history-dependent inverse Gaussian process and derive from it an explicit probability density that gives new definitions of heart rate and heart rate variability: instantaneous R-R interval and heart rate standard deviations. We estimate the time-varying parameters of the inverse Gaussian model by local maximum likelihood and assess model goodness-of-fit by Kolmogorov-Smirnov tests based on the time-rescaling theorem. We illustrate our new definitions in an analysis of human heartbeat intervals from 10 healthy subjects undergoing a tilt-table experiment. Although several studies have identified deterministic, nonlinear dynamical features in human heartbeat intervals, our analysis shows that a highly accurate description of these series at rest and in extreme physiological conditions may be given by an elementary, physiologically based, stochastic model.

Adult↗

Nonlinear analysis of BP signal. Can it detect malfunctions in BP control?

In the present study, our aim was to evaluate the applicability of the nonlinear technique to the investigation of cardiovascular control. We applied an approach known as the "surrogate data method" to test for nonlinear components in the blood pressure (BP) signal. Our results strongly indicate that there are nonlinear components in the BP time series taken from a Wistar-Kyoto rat (WKY), suggesting that the use of nonlinear methods may provide new information about the BP control system. We developed a procedure appropriate for the stable and reliable calculation of the Grassberger-Procaccia correlation dimension (D) of the arterial BP signal. The saturation value D was 5.48 +/- 0.30 for the WKY group and 5.92 +/- 0.26 for the spontaneously hypertensive rat (SHR) group, with P < 0.001. We also found that in the WKY group D displays a significant response to complete alpha 1 blockade and bleeding, whereas no response is observed in the SHR group. These results imply that differences in the control mechanisms may be detected by the nonlinear dynamics approach both under baseline conditions and when interfering with cardiovascular control.

Adrenergic alpha-Antagonists↗

Mutual information discloses relationship between hemodynamic variables in artificial heart-implanted dogs.

A mutual information (MI) method for assessment of the relationship between hemodynamic variables was proposed and applied to the analysis of heart rate (HR), arterial blood pressure (BP), and renal sympathetic nerve activity (RSNA) in artificial heart-implanted dogs to quantify correlation between these parameters. MI measures the nonlinear as well as linear dependence of two variables. Simulation studies revealed that this MI technique furnishes mathematical features well suited to the investigation of nonlinear dynamics such as the cardiovascular system and can quantify a relationship between two parameters. To constitute a model free of the natural heart, two pneumatically actuated ventricular assist devices were implanted as biventricular bypasses in acute canine experiments. RSNA was detected with the use of bipolar electrodes attached to the renal sympathetic nerve. Analysis of data during control revealed that correlation between HR and RSNA was higher than that between HR and BP and that between RSNA and BP (P < 0.05). Although RSNA seemed to fluctuate noncorrelatedly with BP in higher pacing rates, the MI values between them disclosed their strong correlation. Surprisingly, correlation between RSNA and BP was stronger during a pacing rate of 60 beats/min than during higher pacing rates and control (P < 0. 05). It is suggested that the baroreflex system may be susceptible to pacing rates during the total artificial heart state. We calculated the time delay between HR and RSNA, between RSNA and BP, and between HR and BP by regarding a time delay at which the maximum MI value between each pair of parameters was given as a physiological delay. Our results indicate that RSNA leads BP, BP leads HR, and RSNA leads HR during control (P < 0.05). We conclude that this method could provide a powerful means for measuring correlation of physiological variables.

Algorithms↗

Analysis of errors in parameter estimation with application to physiological systems.

The accuracy of parameter estimation applied to physiological systems is analyzed. The method of analysis is applicable to procedures utilizing minimization of squared output error and a nonlinear dynamic system model. Three major sources of estimation error are described: 1) measurement error, 2) modeling error, and 3) optimization error. Measurement errors affect values used for the system output, the model input, and nonestimated parameters of the model. Modeling errors are due to failure to adequately describe the structure of the system and to numerical errors that occur in the digital computer solution of the model equations. Linearization by use of Taylor series expansions in the region of the nominal solution is used to obtain an expression for the covariance matrix of the parameter estimates in terms of the covariance matrix of each error source. The analysis is applied to the example of cardiac output estimation from respiratory measurements. The results demonstrate that an analysis of system identifiability is not sufficient to ensure usable estimates and that systematic error analysis is essential for assessing the usefulness of parameter estimation techniques.

Cardiac Output↗

A mathematics for physiology.

Nonlinear dynamics gives us a language within which to express the basic concepts of physiology. Form, qualitative change, oscillation, stability, and other biologically important notions find natural expressions in this new mathematical approach. An introduction to qualitative dynamics is sketched, its relevance to physiology is argued, and several examples of its usefulness in providing models and metaphors for describing brain activity are offered.

Animals↗

From intermittency to transitivity in neuropsychobiological flows.

Nonlinear dynamics offers a language for describing many aspects of brain function. Intermittency, alternating periods of periodic and chaotic behavior, and transitivity, the indecomposability of a flow, are discussed here in detail. Applications are suggested to neuropsychobiological phenomena, such as the effects of drugs and other agents.

Animals↗

Low-frequency renal sympathetic nerve activity, arterial BP, stationary "1/f noise," and the baroreflex.

The object of this study is to quantify the very low frequency (i.e., <0.1 Hz) interactions between renal sympathetic nerve activity (SNA) and arterial blood pressure (ABP). Six rats were instrumented for chronic recordings of SNA and ABP. Data were collected 24 h after surgery at 10 kHz for 2-5 h and subsequently compressed to a 1-kHz signal. The power spectra and ordinary coherence were calculated from data epochs up to 1 h in length. The very low frequency spectra for both variables were fitted to a constant times f (-beta). The peak magnitude squared of the coherence near 0.4 Hz was 0.82 +/- 0.08, but the apparent linear coherence fell off quickly at lower frequencies so that it was close to zero for frequencies <0.1 Hz. Moreover, at these low frequencies beta, as computed by a coarse grain spectral analysis, was significantly (P < 0.01) different for SNA (0.66 +/- 0.12) and ABP (1.12 +/- 0.14). Assuming that SNA and ABP are stationary time series, the results of our classical spectral analysis would indicate that SNA and ABP are not linearly correlated at frequencies with a period more than approximately 10 s. Accordingly, we tested for stationarity by computing the spectral coherence and found that SNA and ABP are not stationary "1/f noise" within the frequency range from 0.02 to 2.0 Hz. Rather the SNA exerts control over the cardiovascular system through intermittent bursts of activity. Such intermittent behavior can be modeled by nonlinear dynamics.

Animals↗

Effects of head-down bed rest on complex heart rate variability: response to LBNP testing.

Head-down bed rest is used to model physiological changes during spaceflight. We postulated that bed rest would decrease the degree of complex physiological heart rate variability. We analyzed continuous heart rate data from digitized Holter recordings in eight healthy female volunteers (age 28-34 yr) who underwent a 13-day 6 degree head-down bed rest study with serial lower body negative pressure (LBNP) trials. Heart rate variability was measured on 4-min data sets using conventional time and frequency domain measures as well as with a new measure of signal "complexity" (approximate entropy). Data were obtained pre-bed rest (control), during bed rest (day 4 and day 9 or 11), and 2 days post-bed rest (recovery). Tolerance to LBNP was significantly (P < 0.02) reduced on both bed rest days vs. pre-bed rest. Heart rate variability was assessed at peak LBNP. Heart rate approximate entropy was significantly (P < 0.05) decreased at day 4 and day 9 or 11, returning toward normal during recovery. Heart rate standard deviation and the ratio of high- to low-power frequency did not change significantly. We conclude that short-term bed rest is associated with a decrease in the complex variability of heart rate during LBNP testing in healthy young adult women. Measurement of heart rate complexity, using a method derived from nonlinear dynamics ("chaos theory"), may provide a sensitive marker of this loss of physiological variability, complementing conventional time and frequency domain statistical measures.

Adult↗

The neuromuscular transform constrains the production of functional rhythmic behaviors.

We continue our study of the properties and the functional role of the neuromuscular transform (NMT). The NMT is an input-output relation that formalizes the processes by which patterns of motor neuron firing are transformed to muscle contractions. Because the NMT acts as a dynamic, nonlinear, and modifiable filter, the transformation is complex. In the preceding paper we developed a framework for analysis of the NMT and identified with it principles by which the NMT transforms different firing patterns to contractions. The ultimate question is functional, however. In sending different firing patterns through the NMT, the nervous system is seeking to command different functional behaviors, with specific contraction requirements. To what extent do the contractions that emerge from the NMT actually satisfy those requirements? In this paper we extend our analysis to address this issue. We define representative behavioral tasks and corresponding measures of performance, for a single neuromuscular unit, for two antagonistic units, and, in a real illustration, for the accessory radula closer (ARC)-opener neuromuscular system of Aplysia. We focus on cyclical, rhythmic behaviors which reveal the underlying principles particularly clearly. We find that, although every pattern of motor neuron firing produces some state of muscle contraction, only a few patterns produce functional behavior, and even fewer produce efficient functional behavior. The functional requirements thus dictate certain patterns to the nervous system. But many desirable functional behaviors are not possible with any pattern. We examine, in particular, how rhythmic behaviors degrade and disintegrate as the nervous system attempts to speed up their cycle frequency. This happens because, with fixed properties, the NMT produces only a limited range of contraction shapes that are kinetically well matched to the firing pattern only on certain time scales. Thus the properties of the NMT constrain and restrict the production of functional behaviors. In the following paper, we see how the constraint may be alleviated and the range of functional behaviors expanded by appropriately tuning the properties of the NMT through neuromuscular plasticity and modulation.

Animals↗

Modes of baroreceptor-sympathetic coordination.

We tested the hypothesis that the cardiac-related rhythm in sympathetic nerve discharge (SND) results from the forcing of a central oscillator to the frequency of the heart beat by pulse-synchronous baroreceptor afferent nerve activity. For this purpose, time series analysis was used to examine the phase relations between the brachial arterial pulse (AP) and cardiac-related activity recorded from the postganglionic inferior cardiac sympathetic nerve (CN) in urethan-anesthetized cats. Specifically, we made cycle-by-cycle measurements of peak systolic blood pressure, heart period, CN burst amplitude, and the phase angle (and corresponding interval) between peak systole and the next peak of CN activity. As the steady-state level of systolic blood pressure was raised by increasing the rate of a constant intravenous infusion of phenylephrine, we observed transitions from no phase-locking of CN activity to the AP to either phase-locking of variable strength or phase walk through part of the cardiac-cycle on the time scale of respiration. Phase walk is defined as a progressive and systematic change in the phase lag of cardiac-related CN activity relative to peak systole. Raising blood pressure strengthened phase-locking and either increased or decreased the mean interval between peak systole and the next peak of CN activity even when the change in heart period was small. CN burst amplitude and the interval between peak systole and the next peak of CN activity were inversely related, but the strength of the relationship varied considerably with experimental conditions. The relationship was strongest during phase walk. Step-wise increases in blood pressure induced by abdominal aortic obstruction led to an abrupt increase in the phase lag of CN activity relative to peak systole even when heart rate was not changed. We refer to such changes as sharp phase transitions that are a general property of dynamical nonlinear systems. The results support the view that the cardiac-related rhythm in SND is a forced nonlinear oscillation rather than the consequence of periodic inhibition of randomly generated activity.

Animals↗

PhysioBank, PhysioToolkit, and PhysioNet: components of a new research resource for complex physiologic signals.

The newly inaugurated Research Resource for Complex Physiologic Signals, which was created under the auspices of the National Center for Research Resources of the National Institutes of Health, is intended to stimulate current research and new investigations in the study of cardiovascular and other complex biomedical signals. The resource has 3 interdependent components. PhysioBank is a large and growing archive of well-characterized digital recordings of physiological signals and related data for use by the biomedical research community. It currently includes databases of multiparameter cardiopulmonary, neural, and other biomedical signals from healthy subjects and from patients with a variety of conditions with major public health implications, including life-threatening arrhythmias, congestive heart failure, sleep apnea, neurological disorders, and aging. PhysioToolkit is a library of open-source software for physiological signal processing and analysis, the detection of physiologically significant events using both classic techniques and novel methods based on statistical physics and nonlinear dynamics, the interactive display and characterization of signals, the creation of new databases, the simulation of physiological and other signals, the quantitative evaluation and comparison of analysis methods, and the analysis of nonstationary processes. PhysioNet is an on-line forum for the dissemination and exchange of recorded biomedical signals and open-source software for analyzing them. It provides facilities for the cooperative analysis of data and the evaluation of proposed new algorithms. In addition to providing free electronic access to PhysioBank data and PhysioToolkit software via the World Wide Web (http://www.physionet. org), PhysioNet offers services and training via on-line tutorials to assist users with varying levels of expertise.

Databases as Topic↗