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PubMed2004

Chaotic electron diffusion through stochastic webs enhances current flow in superlattices.

Understanding how complex systems respond to change is of fundamental importance in the natural sciences. There is particular interest in systems whose classical newtonian motion becomes chaotic as an applied perturbation grows. The transition to chaos usually occurs by the gradual destruction of stable orbits in parameter space, in accordance with the Kolmogorov-Arnold-Moser (KAM) theorem--a cornerstone of nonlinear dynamics that explains, for example, gaps in the asteroid belt. By contrast, 'non-KAM' chaos switches on and off abruptly at critical values of the perturbation frequency. This type of dynamics has wide-ranging implications in the theory of plasma physics, tokamak fusion, turbulence, ion traps, and quasicrystals. Here we realize non-KAM chaos experimentally by exploiting the quantum properties of electrons in the periodic potential of a semiconductor superlattice with an applied voltage and magnetic field. The onset of chaos at discrete voltages is observed as a large increase in the current flow due to the creation of unbound electron orbits, which propagate through intricate web patterns in phase space. Non-KAM chaos therefore provides a mechanism for controlling the electrical conductivity of a condensed matter device: its extreme sensitivity could find applications in quantum electronics and photonics.

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PubMed2005

Host immunity and synchronized epidemics of syphilis across the United States.

A central question in population ecology is the role of 'exogenous' environmental factors versus density-dependent 'endogenous' biological factors in driving changes in population numbers. This question is also central to infectious disease epidemiology, where changes in disease incidence due to behavioural or environmental change must be distinguished from the nonlinear dynamics of the parasite population. Repeated epidemics of primary and secondary syphilis infection in the United States over the past 50 yr have previously been attributed to social and behavioural changes. Here, we show that these epidemics represent a rare example of unforced, endogenous oscillations in disease incidence, with an 8-11-yr period that is predicted by the natural dynamics of syphilis infection, to which there is partially protective immunity. This conclusion is supported by the absence of oscillations in gonorrhoea cases, where a protective immune response is absent. We further demonstrate increased synchrony of syphilis oscillations across cities over time, providing empirical evidence for an increasingly connected sexual network in the United States.

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PubMed2005

Possible solar origin of the 1,470-year glacial climate cycle demonstrated in a coupled model.

Many palaeoclimate records from the North Atlantic region show a pattern of rapid climate oscillations, the so-called Dansgaard-Oeschger events, with a quasi-periodicity of approximately 1,470 years for the late glacial period. Various hypotheses have been suggested to explain these rapid temperature shifts, including internal oscillations in the climate system and external forcing, possibly from the Sun. But whereas pronounced solar cycles of approximately 87 and approximately 210 years are well known, a approximately 1,470-year solar cycle has not been detected. Here we show that an intermediate-complexity climate model with glacial climate conditions simulates rapid climate shifts similar to the Dansgaard-Oeschger events with a spacing of 1,470 years when forced by periodic freshwater input into the North Atlantic Ocean in cycles of approximately 87 and approximately 210 years. We attribute the robust 1,470-year response time to the superposition of the two shorter cycles, together with strongly nonlinear dynamics and the long characteristic timescale of the thermohaline circulation. For Holocene conditions, similar events do not occur. We conclude that the glacial 1,470-year climate cycles could have been triggered by solar forcing despite the absence of a 1,470-year solar cycle.

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PubMed2003

Assessment of cardiovascular reactivity by fractal and recurrence quantification analysis of heart rate and pulse transit time.

Methods used for the assessment of cardiovascular reactivity are flawed by nonlinear dynamics of the cardiovascular responses to stimuli. In an attempt to address this issue, we utilized a short postural challenge, recorded beat-to-beat heart rate (HR) and pulse transit time (PTT), assessed the data by fractal and recurrence quantification analysis, and processed the obtained variables by multivariate statistics. A 10-min supine phase of the head-up tilt test was followed by recording 600 cardiac cycles on tilt, that is, 5-10 min. Three groups of patients were studied, each including 20 subjects matched for age and gender--healthy subjects, patients with essential hypertension (HT), and patients with chronic fatigue syndrome (CFS). The latter group was studied on account of the well-known dysautonomia of CFS patients, which served as contrast against the cardiovascular reactivity of the healthy population. A total of 52 variables of the HR and PTT were determined in each subject. The multivariate model identified the best predictors for the assessment of reactivity of healthy subjects vs CFS. Based on these predictors, the "Fractal & Recurrence Analysis-based Score" (FRAS) was calculated: FRAS=76.2+0.04*HR-supine-DET -12.9*HR-tilt-R/L -0.31*HR-tilt-s.d. -19.27*PTT-tilt-R/L -9.42*PTT-tilt-WAVE. The median values and IQR of FRAS in the groups were: healthy=-1.85 (IQR 1.89), hypertensives=+0.52 (IQR 5.78), and CFS=-24.2 (5.34) (HT vs healthy subjects: P=0.0036; HT vs CFS: P<0.0001). Since the FRAS differed significantly between the three groups, it appears likely that the FRAS may recognize phenotypes of cardiovascular reactivity.

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PubMed2004

Baroreflex sensitivity, heart rate, and blood pressure variability in hypertensive pregnancy disorders.

Hypertensive pregnancy disorders are a leading cause of perinatal and maternal morbidity and mortality. Heart rate variability (HRV), blood pressure variability (BPV), and baroreflex sensitivity (BRS) are relevant predictors of cardiovascular risk in humans. The aim of the study was to evaluate whether HRV, BPV, and BRS differ between distinct hypertensive pregnancy disorders. Continuous heart rate and blood pressure recordings were performed in 80 healthy pregnant women as controls (CON), 19 with chronic hypertension (CH), 18 with pregnancy-induced hypertension (PIH), and 44 with pre-eclampsia (PE). The data were assessed by time and frequency domain analysis, nonlinear dynamics, and BRS. BPV is markedly altered in all three groups with hypertensive disorders compared to healthy pregnancies, whereby changes were most pronounced in PE patients. Interestingly, this increase in PE patients did not lead to elevated spontaneous baroreflex events, while BPV changes in both the other hypertensive groups were paralleled by alterations in baroreflex parameters. The HRV is unaltered in CH and PE but significantly impaired in PIH. We conclude that parameters of the HRV, BPV, and BRS differ between various hypertensive pregnancy disorders. Thus, distinct clinical manifestations of hypertension in pregnancy have different pathophysiological, regulatory, and compensatory mechanisms.

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PubMed2002

Evaluation of the responses of a semiconductor gas sensor to gaseous mixtures under the application of temperature modulation.

A novel gas-sensing system based on a dynamic nonlinear response is reported to evaluate the effect of gaseous mixtures on the sensor response. A sinusoidal temperature perturbation was applied to a semiconductor gas sensor and the resulting conductance of the sensor was analyzed by fast Fourier transformation (FFT). The sensor response, which changed characteristically depending on the composition of the gaseous mixture, could be classified into three types (enhanced, suppressed, and preferential responses) by the mixture. To monitor the progress of the reaction of gases, the sample gas was analyzed by gas chromatography. The coexistent effect on the response to gaseous mixtures was theoretically simulated by considering the kinetics of gas molecules on the semiconductor surface.

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PubMed2003

[Analysis of ventricular fibrillation signals for the evaluation of defibrillation success in the treatment of ventricular fibrillation].

OBJECTIVE: Precise detection of ventricular fibrillation (VF), reliable prediction of defibrillation success and adjustment of the discharge waveform to the patient's transthoracic impedance may contribute to a reduction of electricity-associated myocardial injury caused by unnecessary counter shocks. Specifically, asystole thresholds distinguish between VF and asystole, and thus prevent unnecessary defibrillation attempts. We reviewed various studies and manufacturer characteristics regarding the parameters and algorithms for analyzing arrhythmia ECG signals. METHODS: Asystole threshold values of several defibrillator manufacturers were collected and a literature review was performed including the following parameters: amplitude, frequency, bispectral analysis, amplitude spectrum area, wavelets, nonlinear dynamics, N(alpha)histograms, and combinations of various parameters. RESULTS: The manufacturer dependent asystole thresholds vary substantially. We show ways to optimize an ECG-based analysis for the next technological generation of defibrillators. During advanced cardiac life support (ACLS) the probability of defibrillation success should be estimated. Optimal defibrillation waveform, depending on transthoracic resistance, should be individually determined. In case of prolonged VF with a low ECG amplitude defibrillation should not be attempted unless coronary perfusion has been improved by further measures of ACLS. The combined evaluation of VF amplitude and frequency is effective in predicting defibrillation success. Estimation of further parameters is potentially useful for guiding optimal timing of defibrillation. At present, the implementation of most parameters in out-of-hospital cardiopulmonary resuscitation (CPR) is limited by the lack of technical feasibility of online computing. CONCLUSION: Analysis of VF ECG signals should allow adequate VF detection as well as prediction of defibrillation success. Suitable asystole thresholds for analysis of ECG signals have to be determined, and the adverse effects of CPR associated artefacts on data analysis have to be reduced. Analysis of VF ECG signals is a precondition of individually optimized defibrillation and may contribute substantially to an increased quality of CPR.

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PubMed1995

Nonlinearity of heart rate in the neonate.

The relationship between heart rate variability and level of illness was examined. Fifteen patients (10 male and 5 female), gestational ages 25 to 42 weeks, postnatal ages 1 to 42 days, birthweights 545 to 4375 g receiving care in the neonatal intensive care nursery were randomly selected. Data from each infant was transferred from the bedside physiologic monitor to a microcomputer for analysis. A severity of illness index (the Children's Hospital Illness Score [CHILLS]) correlated with heart rate variability. Four patterns of heart rate variability were identified: (1) infants whose CHILLS score indicated that they were cardiovascularly normal demonstrated a modest amount of variability; (2) infants with a CHILLS score indicating a moderate amount of illness had heart rates and heart rate variability greater than the normal infants; (3) three infants exhibited bimodality (period doubling) in their heart rates; each of these infants had a CHILLS score that indicated that they were less ill than the most critically ill patients, but sicker than those moderately ill infants without period doubling; and (4) heart rate decreased in the most critically ill infants identified by the CHILLS, but it remained above the heart rate of a healthy newborn; heart rate variability collapsed below that of a healthy newborn. Our data suggest that the variability of heart rate may increase as an infant becomes sicker. When the infant becomes critically ill and unstable, heart rate variability is less than the normal infant. Nonlinear dynamics theory may be a potential model for fitting the data.

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PubMed2001

Designer gene networks: Towards fundamental cellular control.

The engineered control of cellular function through the design of synthetic genetic networks is becoming plausible. Here we show how a naturally occurring network can be used as a parts list for artificial network design, and how model formulation leads to computational and analytical approaches relevant to nonlinear dynamics and statistical physics. We first review the relevant work on synthetic gene networks, highlighting the important experimental findings with regard to genetic switches and oscillators. We then present the derivation of a deterministic model describing the temporal evolution of the concentration of protein in a single-gene network. Bistability in the steady-state protein concentration arises naturally as a consequence of autoregulatory feedback, and we focus on the hysteretic properties of the protein concentration as a function of the degradation rate. We then formulate the effect of an external noise source which interacts with the protein degradation rate. We demonstrate the utility of such a formulation by constructing a protein switch, whereby external noise pulses are used to switch the protein concentration between two values. Following the lead of earlier work, we show how the addition of a second network component can be used to construct a relaxation oscillator, whereby the system is driven around the hysteresis loop. We highlight the frequency dependence on the tunable parameter values, and discuss design plausibility. We emphasize how the model equations can be used to develop design criteria for robust oscillations, and illustrate this point with parameter plots illuminating the oscillatory regions for given parameter values. We then turn to the utilization of an intrinsic cellular process as a means of controlling the oscillations. We consider a network design which exhibits self-sustained oscillations, and discuss the driving of the oscillator in the context of synchronization. Then, as a second design, we consider a synthetic network with parameter values near, but outside, the oscillatory boundary. In this case, we show how resonance can lead to the induction of oscillations and amplification of a cellular signal. Finally, we construct a toggle switch from positive regulatory elements, and compare the switching properties for this network with those of a network constructed using negative regulation. Our results demonstrate the utility of model analysis in the construction of synthetic gene regulatory networks. (c) 2001 American Institute of Physics.

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PubMed2001

Molecular, metabolic, and genetic control: An introduction.

The living cell is a miniature, self-reproducing, biochemical machine. Like all machines, it has a power supply, a set of working components that carry out its necessary tasks, and control systems that ensure the proper coordination of these tasks. In this Special Issue, we focus on the molecular regulatory systems that control cell metabolism, gene expression, environmental responses, development, and reproduction. As for the control systems in human-engineered machines, these regulatory networks can be described by nonlinear dynamical equations, for example, ordinary differential equations, reaction-diffusion equations, stochastic differential equations, or cellular automata. The articles collected here illustrate (i) a range of theoretical problems presented by modern concepts of cellular regulation, (ii) some strategies for converting molecular mechanisms into dynamical systems, (iii) some useful mathematical tools for analyzing and simulating these systems, and (iv) the sort of results that derive from serious interplay between theory and experiment. (c) 2001 American Institute of Physics.

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PubMed2002

Coherent structures and self-consistent transport in a mean field Hamiltonian model.

A study of coherent structures and self-consistent transport is presented in the context of a Hamiltonian mean field, single wave model. The model describes the weakly nonlinear dynamics of marginally stable plasmas and fluids, and it is related to models of systems with long-range interactions in statistical mechanics. In plasma physics the model applies to the interaction of electron "holes" and electron "clumps," which are depletions and excesses of phase-space electron density with respect to a fixed background. In fluid dynamics the system describes the interaction of vortices with positive and negative circulation in a two-dimensional background shear flow. Numerical simulations in the finite-N and in the N--> infinity kinetic limit (where N is the number of particles) show the existence of coherent, rotating dipole states. We approximate the dipole as two "macroparticles" (one hole and one clump) and consider the N=2 limit of the model. We show that this limit has a family of symmetric, rotating integrable solutions described by a one-degree-of-freedom nontwist Hamiltonian. A perturbative solution of the nontwist Hamiltonian provides an accurate description of the mean field and rotation period of the dipole. The coherence of the dipole is explained in terms of a parametric resonance between the rotation frequency of the macroparticles and the oscillation frequency of the self-consistent mean field. This resonance creates islands of integrability that shield the dipole from regions of chaotic transport. For a class of initial conditions, the mean field exhibits an elliptic-hyperbolic bifurcation that leads to the filamentation, chaotic mixing and eventual destruction of the dipole. (c) 2002 American Institute of Physics.

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PubMed1993

Predictability of normal heart rhythms and deterministic chaos.

The evidence for deterministic chaos in normal heart rhythms is examined. Electrocardiograms were recorded of 29 subjects falling into four groups-a young healthy group, an older healthy group, and two groups of patients who had recently suffered an acute myocardial infarction. From the measured R-R intervals, a time series of 1000 first differences was constructed for each subject. The correlation integral of Grassberger and Procaccia was calculated for several subjects using these relatively short time series. No evidence was found for the existence of an attractor having a dimension less than about 4. However, a prediction method recently proposed by Sugihara and May and an autoregressive linear predictor both show that there is a measure of short-term predictability in the differenced R-R intervals. Further analysis revealed that the short-term predictability calculated by the Sugihara-May method is not consistent with the null hypothesis of a Gaussian random process. The evidence for a small amount of nonlinear dynamical behavior together with the short-term predictability suggest that there is an element of deterministic chaos in normal heart rhythms, although it is not strong or persistent. Finally, two useful parameters of the predictability curves are identified, namely, the 'first step predictability' and the 'predictability decay rate,' neither of which appears to be significantly correlated with the standard deviation of the R-R intervals.

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PubMed1995

Quantitative analysis of heart rate variability.

In the modern industrialized countries every year several hundred thousands of people die due to sudden cardiac death. The individual risk for this sudden cardiac death cannot be defined precisely by common available, noninvasive diagnostic tools like Holter monitoring, highly amplified ECG and traditional linear analysis of heart rate variability (HRV). Therefore, we apply some rather unconventional methods of nonlinear dynamics to analyze the HRV. Especially, some complexity measures that are based on symbolic dynamics as well as a new measure, the renormalized entropy, detect some abnormalities in the HRV of several patients who have been classified in the low risk group by traditional methods. A combination of these complexity measures with the parameters in the frequency domain seems to be a promising way to get a more precise definition of the individual risk. These findings have to be validated by a representative number of patients. (c) 1995 American Institute of Physics.

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PubMed1995

Nonlinear time series analysis of electrocardiograms.

In recent years there has been an increasing number of papers in the literature, applying the methods and techniques of Nonlinear Dynamics to the time series of electrical activity in normal electrocardiograms (ECGs) of various human subjects. Most of these studies are based primarily on correlation dimension estimates, and conclude that the dynamics of the ECG signal is deterministic and occurs on a chaotic attractor, whose dimension can distinguish between healthy and severely malfunctioning cases. In this paper, we first demonstrate that correlation dimension calculations must be used with care, as they do not always yield reliable estimates of the attractor's "dimension." We then carry out a number of additional tests (time differencing, smoothing, principal component analysis, surrogate data analysis, etc.) on the ECGs of three "normal" subjects and three "heavy smokers" at rest and after mild exercising, whose cardiac rhythms look very similar. Our main conclusion is that no major dynamical differences are evident in these signals. A preliminary estimate of three to four basic variables governing the dynamics (based on correlation dimension calculations) is updated to five to six, when temporal correlations between points are removed. Finally, in almost all cases, the transition between resting and mild exercising seems to imply a small increase in the complexity of cardiac dynamics. (c) 1995 American Institute of Physics.

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PubMed1996

The dripping faucet revisited.

High accuracy experimental results on the nonlinear dynamical behaviour of a dripping faucet are presented. The distribution functions for droplet sizes and drip intervals together with return maps are studied for various dripping rates. Increasing this control parameter, chaotic behaviour is obtained and discussed. (c) 1996 American Institute of Physics.

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PubMed1996

Statistical measures derived from the correlation integrals of physiological time series.

In this work correlation integrals are used for the analysis of various EEG signals from rabbits in resting states and under the influence of an anesthetic. The comparison with surrogate data reveals nonlinear dynamics in all of the time series. Our attempt to determine the correlation dimension D(2) by the modified algorithm of Theiler [Phys. Rev. A 34, 2427 (1986)] failed since no saturation is reached with increasing embedding dimension. The hypothesis of low-dimensional chaos turns out to be inconsistent with our results, but we can still distinguish, at least qualitatively, between different states of brain dynamics. A quantitative characterization of the time series is possible by defining correlation parameters P(a) derived from correlation integrals reflecting also autocorrelation of the signal. (c) 1996 American Institute of Physics.

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PubMed1997

Multistability and the control of complexity.

We show how multistability arises in nonlinear dynamics and discuss the properties of such a behavior. In particular, we show that most attractors are periodic in multistable systems, meaning that chaotic attractors are rare in such systems. After arguing that multistable systems have the general traits expected from a complex system, we pass to control them. Our controlling complexity ideas allow for both the stabilization and destabilization of any one of the coexisting states. The control of complexity differs from the standard control of chaos approach, an approach that makes use of the unstable periodic orbits embedded in an extended chaotic attractor. (c) 1997 American Institute of Physics.

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PubMed1997

Generalized entropies of chaotic maps and flows: A unified approach.

A thermodynamic study of nonlinear dynamical systems, based on the orbits' return times to the elements of a generating partition, is proposed. Its grand canonical nature makes it suitable for application to both maps and flows, including autonomous ones. When specialized to the evaluation of the generalized entropies K(q), this technique reproduces a well-known formula for the metric entropy K(1) and clarifies the relationship between a flow and the associated Poincare maps, beyond the straightforward case of periodically forced nonautonomous systems. Numerical estimates of the topological and metric entropy are presented for the Lorenz and Rossler systems. The analysis has been carried out exclusively by embedding scalar time series, ignoring any further knowledge about the systems, in order to illustrate its usefulness for experimental signals as well. Approximations to the generating partitions have been constructed by locating the unstable periodic orbits of the systems up to order 9. The results agree with independent estimates obtained from suitable averages of the local expansion rates along the unstable manifolds. (c) 1997 American Institute of Physics.

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