[Use of nonlinear dynamics methods for detecting and describing chaotic deterministic EEG components].
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Animals↗
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Results for “Nonlinear Dynamics”
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[Nonlinear dynamics in regulation of heart rate in healthy infants].
The aim of this study was to investigate qualitatively and quantitatively non-linear and linear characteristics of heart rate identifying their connection to sleep states during the first 6 months of life. 16 newborns were examined polygraphically in a longitudinal study (first day, first and sixth month). After R-peak detection of a limb lead ECG and R-R interval calculation, time series of the instantaneous heart rate (IHR) were constructed. They were analyzed qualitatively with regard to the structure of the Poincaré maps and the occurrence of bifurcations as well as quantitatively by calculating the correlation dimension (D2) and the Lyapunov exponent (LLE). In some cases, bifurcations in the IHR time series occurred. The Poincaré maps showed mainly clear structures in the shape of limited point clusters. D2 was in the range of 1.5 to 2.5 and was larger in quiet than in active sleep. LLE was always positive, although higher values in active sleep than in quiet sleep were exhibited in the first month of life only. D2 and LLE values during active sleep were age-dependent. The results of the study indicate a non-linear component in the heart rate control of healthy newborns. The change in D2 and LLE in connection with postnatal age and sleep states expresses a modulation of these system components during the postnatal maturation and during vegetative sleep organisation.
Child Development↗
Geometrical techniques for analyzing ECG dynamics.
Nonlinear dynamical systems theory motivates a new class of techniques for analyzing signals, based on the idea of converting a signal into a geometrical object--a "trajectory" in a reconstructed "state space." This paper discusses one such technique for detecting and quantifying electrical alternans.
Electrocardiography↗
Slow dynamics and anomalous nonlinear fast dynamics in diverse solids.
Results are reported of the first systematic study of anomalous nonlinear fast dynamics and slow dynamics in a number of solids. Observations are presented from seven diverse materials showing that anomalous nonlinear fast dynamics (ANFD) and slow dynamics (SD) occur together, significantly expanding the nonlinear mesoscopic elasticity class. The materials include samples of gray iron, alumina ceramic, quartzite, cracked Pyrex, marble, sintered metal, and perovskite ceramic. In addition, it is shown that materials which exhibit ANFD have very similar ratios of amplitude-dependent internal-friction to the resonance-frequency shift with strain amplitude. The ratios range between 0.28 and 0.63, except for cracked Pyrex glass, which exhibits a ratio of 1.1, and the ratio appears to be a material characteristic. The ratio of internal friction to resonance frequency shift as a function of time during SD is time independent, ranging from 0.23 to 0.43 for the materials studied.
Elasticity↗
Disentangling extrinsic from intrinsic factors in disease dynamics: a nonlinear time series approach with an application to cholera.
Alternative explanations for disease and other population cycles typically include extrinsic environmental drivers, such as climate variability, and intrinsic nonlinear dynamics resulting from feedbacks within the system, such as species interactions and density dependence. Because these different factors can interact in nonlinear systems and can give rise to oscillations whose frequencies differ from those of extrinsic drivers, it is difficult to identify their respective contributions from temporal population patterns. In the case of disease, immunity is an important intrinsic factor. However, for many diseases, such as cholera, for which immunity is temporary, the duration and decay pattern of immunity is not well known. We present a nonlinear time series model with two related objectives: the reconstruction of immunity patterns from data on cases and population sizes and the identification of the respective roles of extrinsic and intrinsic factors in the dynamics. Extrinsic factors here include both seasonality and long-term changes or interannual variability in forcing. Results with simulated data show that this semiparametric method successfully recovers the decay of immunity and identifies the origin of interannual variability. An application to historical cholera data indicates that temporary immunity can be long-lasting and decays in approximately 9 yr. Extrinsic forcing of transmissibility is identified to have a strong seasonal component along with a long-term decrease. Furthermore, noise appears to sustain the multiple frequencies in the long-term dynamics. Similar semiparametric models should apply to population data other than for disease.
Cholera↗
A method for constructing data-based models of spiking neurons using a dynamic linear-static nonlinear cascade.
This paper describes a general nonlinear dynamical model for neural system identification. It describes an algorithm for fitting a simple form of the model to spike train data, and reports on this algorithm's performance in identifying the structure and parameters of simulated neurons. The central element of the model is a Wiener-Bose dynamic nonlinearity that ensures that the model is able to approximate the behaviour of an arbitrary nonlinear dynamical system. Nonlinearities associated with spike generation and transmission are treated by placing the Wiener-Bose system in cascade with pulse frequency modulators and demodulators, and the static nonlinearity at the output of the Wiener-Bose system is decomposed into a rectifier and a multinomial. This simplifies the model without reducing its generality for neuronal system identification. Model elements can be characterised using standard methods of dynamical systems analysis, and the model has a simple form that can be implemented and simulated efficiently. This model bears a structural resemblance to real neurons; it may be regarded as a connectionist "neuron" that has been generalized in a realistic way to enable it to mimic the behaviour of an arbitrary nonlinear system, or conversely as a general nonlinear model that has been constrained to make it easy to fit to spike train data. Tests with simulated data show that the identification algorithm can accurately estimate the structure and parameters of neuron-like nonlinear dynamical systems using data sets containing only a few hundred spikes.
Animals↗
"Biospheric medicine" as viewed from the two-year first closure of Biosphere 2.
Biosphere 2 is a 3.15-acre, 7-million ft. enclosed ecological space near Tucson, AZ. It contains five wilderness and two domestic biomes (rain forest, savanna, desert, ocean, marsh; agricultural station, living quarters), an original introduction of 3,800 species (approximately 20% extinctions have occurred), and a large basement "technosphere." Sealed inside Biosphere 2 in September 1991, four women and four men, including two of the authors, maintained themselves and the various systems for 2 yr, the longest-sustained "isolated confined environment" period on record. MMPI psychological profile scores for Biosphere 2 crewmembers correlated closely with those reported for astronauts and shuttle applicants. Major medical problems encountered during the 2 yr included adaptation to a low-calorie (1800-2200 kcal.d-1 per person) but otherwise nutritionally adequate diet, with substantial weight loss (18% for men, 10% for women), and a declining oxygen atmosphere (down to 14.2%). Life in a miniworld such as Biosphere 2 may differ substantially from life in a space station or temporary planetary base. These differences include multiple, shifting, sometimes opposing post-launch objectives; complete self-sustenance with recycling of virtually all materials within a highly complex biologic system; retooling of some areas of practical medicine; an attention to "culture" as a social dynamic and how that may influence crew and leadership selection in a societal rather than a quasi-military community. Assuming that long-term planetary colonies must be largely self-sustaining (due to costs of supply over great distances), they must of necessity approach the condition of biospheres. Subject to chaos dynamic (nonlinear dynamic) perturbations, the behavior of complex biospheres will be inherently non-predictable--as opposed to the linear dynamic situation of most space missions--and will require of the inhabitants, including the medical team, a wide range of coping abilities. Under the circumstances, and while strong similarities exist, important differences may serve to distinguish "biospheric medicine" from "space medicine."
Adaptation, Psychological↗
Principal dynamic mode analysis of nonlinear transduction in a spider mechanoreceptor.
The nonlinear dynamics of the mechanoelectrical transduction in an arthropod mechanoreceptor (cuticular slit sense organ of the spider Cupiennius salei) were studied using Volterra kernel measurements and the recently proposed method of principal dynamic modes. Since mechanoreceptors must operate with sufficient gain sensitivity to rapidly varying displacement stimuli over a broad bandwidth and for a wide range of amplitudes, the experimental data were generated by applying pseudorandom broadband mechanical displacements of various mean levels to the cuticular slits. The recorded response data were intracellular current and potential. The purpose of this paper is to demonstrate the use of the principal dynamic mode (PDM) methodology in elucidating the nonlinear dynamics of a spider mechanoreceptor. The results obtained demonstrate that two PDMs suffice to provide a complete nonlinear dynamic model of this insect mechanoreceptor. The first PDM resembles the first-order kernel and has a low pass characteristic (position dependent), while the second PDM has a high-pass characteristic (velocity-dependent) and resides entirely in the second-order kernel (nonlinear adaptation). This study may serve as an example of the proper use of this new methodology for the analysis of nonlinear physiological systems.
Animals↗
Self-induced chaos in a single-mode inversionless laser.
A single-mode inversionless laser with a three-level phaseonium as an active medium can by itself exhibit complex nonlinear dynamics. Nonlinear interaction between two spectrally separated gain regions of the phaseonium and a lasing field gives rise to instabilities and chaotic self-pulsations of a type not observed in conventional lasers with population-inverted gain media. We calculate the bifurcation diagram and uncover multistability and a torus-doubling cascade in transition to chaos.
Journal Article↗
Power spectra reveal the influence of stochasticity on nonlinear population dynamics.
Stochasticity alters the nonlinear dynamics of inherently cycling populations. The power spectrum can describe and explain the impacts of stochasticity. We fitted models to short observed time series of flour beetle populations in the frequency domain, then used a well fitting stochastic mechanistic model to generate detailed predictions of population spectra. Some predicted spectral peaks represent periodic phenomena induced or modified by stochasticity and were experimentally confirmed. For one experimental treatment, linearization theory explained that these peaks represent overcompensatory decay of deviations from deterministic oscillation. In another treatment, stochasticity caused frequent directional phase shifting around a cyclic attractor. This directional phase shifting was not explained by linearization theory and modified the periodicity of the system. If field systems exhibit directional phase shifting, then changing the intensity of demographic or environmental noise while holding constant the structure of the noise can change the main frequency of population fluctuations.
Animals↗
[Complexity analysis of surface EMG signals].
OBJECTIVE: Since the neurophysiological system is a highly nonlinear dynamic system, nonlinear dynamic information of EMG signals were extracted to describe its characteristics. METHOD: Two-channel surface EMG signals were extracted and analyzed to reflect the complexity degree of the dynamics of the neurophysiological system. RESULT: Complexity measures of four kinds of forearm motions were calculated and compared. They showed a good separability. CONCLUSION: Experimental results proved that this measure, having a simple algorithm, is suitable for short data sets and suitable for real time processing. It provides a new measurable index for both physiological and pathological analysis.
Electromyography↗
Nonlinear absorption dynamics in tetrapyridyl metalloporphyrins.
Nonlinear absorption dynamics of Zn(2+), Cu(2+), and Ni(2+) tetrapyridyl porphyrins in chloroform/methanol solutions were investigated at 532 nm with the Z-scan technique. Additional techniques such as UV-vis absorption spectroscopy and time-resolved fluorescence were used to obtain parameters that are important for the analysis of the population dynamics. A marked difference was observed in the nonlinear absorption and excited-state dynamics of closed (ZnTPyP)- and open-shell metalloporphyrins (CuTPyP and NiTPyP). ZnTPyP presents a reverse saturable absorption whose dynamics can be completely described by means of a simple five-energy-level diagram. On the other hand, CuTPyP and NiTPyP have a different excited-state dynamics, presenting a saturable absorption behavior and faster relaxation rates that were attributed to the presence of unfilled d shells of the central ion.
Metalloporphyrins↗
Nonlinear chaotic dynamics of arterial blood pressure and renal blood flow.
To determine whether arterial pressure (AP) and renal blood flow (RBF) are nonlinear dynamic processes (chaotic), we measured resting AP and RBF over 4 h in six conscious dogs. A catheter was placed in the aorta, and transit-time flowmeters were positioned around the renal artery. The average AP was 102 +/- 3 mmHg, and the mean RBF was 318 +/- 42 ml/min. We applied four analytic procedures to test the nature of AP and RBF time series, i.e., to determine if these variables are controlled randomly, if they consist of periodic oscillations, or whether they are best characterized as nonlinear dynamic processes. To this end, a fast Fourier transform was performed to quantify the amount of distinct periodic oscillations and nonperiodic variability in the very low frequency domain (< 0.01 Hz). The power spectrum of AP and RBF revealed broad band noise with no distinct peaks, which is commonly referred to as "1/f noise." As a second procedure, time-delayed phase return maps were constructed, and as a third approach the correlation dimensions were estimated via the Grassberger-Procaccia algorithm. The correlation dimensions of RBF and AP were similar (RBF 3.3 +/- 0.37 vs. AP 3.6 +/- 0.23; P = 0.2). The fourth method determined sensitive dependence on initial conditions, a hallmark of nonlinear "chaotic" dynamics. We determined the maximal Lyapunov exponents and found them to be positive for AP (0.1 +/- 0.01) and for RBF (0.04 +/- 0.01) indicating that they both are nonlinear dynamic processes.(ABSTRACT TRUNCATED AT 250 WORDS)
Animals↗
Dynamic functional tuning of nonlinear cortical networks.
The mammalian neocortex is a highly complex and nonlinear dynamic system. One of its most prominent features is an omnipresent spontaneous neuronal activity. Here the possible functional role of this global background for cognitive flexibility is studied in a prototypic mean-field model area. It is demonstrated that the level of global background current efficiently controls the stimulus-response threshold and the stability and properties of short-term memory states. Moreover, it can dynamically gate arbitrary cortical subnetworks, when applied to parts of the area as a weak bias signal. These results suggest a central functional role of the level of background activation: the dynamic functional tuning of neocortical circuits.
Action Potentials↗
Nonlinear wave dynamics in Faraday instabilities.
Nonlinear wave dynamics in parametrically driven surface waves are studied in numerical simulations of the two-dimensional Navier-Stokes equation, with an emphasis on the evolution and interaction between different wave number modes. The dynamics are found to be closely correlated with the single-mode nonlinear saturated wave amplitudes. Modulating behavior of primary wave modes in a particular parameter range and in time scales much longer than the underlining wave periods is observed.
Journal Article↗
The Ornstein-Uhlenbeck model for decision time in cognitive tasks: an example of control of nonlinear network dynamics.
The Ornstein-Uhlenbeck (OU) model for human decision-making has been successfully applied to account for response accuracy and response time (RT) data in recent two-choice decision models. A variant of the OU model is shown to arise from the response dynamics of a nonlinear network consisting of randomly connected neural processing units. When feedback control of the network is effected by the stimulus onset, the average network response is an autocorrelated random signal satisfying the stochastic differential equation for the OU process. An alternative, more general, stimulus detection procedure is proposed which involves the use of an adaptive Kalman filter process to track any temporal change in autoregressive parameters. The predicted decision time distributions suggest that both the OU and the Kalman filter processes can serve as alternative models for RT data in experimental tasks.
Cognition↗
The epileptic process as nonlinear deterministic dynamics in a stochastic environment: an evaluation on mesial temporal lobe epilepsy.
The theory of deterministic chaos addresses simple deterministic dynamics in which nonlinearity gives rise to complex temporal behavior. Although biological neuronal networks such as the brain are highly complicated, a number of studies provide growing evidence that nonlinear time series analysis of brain electrical activity in patients with epilepsy is capable of providing potentially useful diagnostic information. In the present study, this analysis framework was extended by introducing a new measure xi, designed to discriminate between nonlinear deterministic and linear stochastic dynamics. For the evaluation of its discriminative power, xi was extracted from intracranial multi-channel EEGs recorded during the interictal state in 25 patients with unilateral mesial temporal lobe epilepsy. Strong indications of nonlinear determinism were found in recordings from within the epileptogenic zone, while EEG signals from other sites mainly resembled linear stochastic dynamics. In all investigated cases, this differentiation allowed to retrospectively determine the side of the epileptogenic zone in full agreement with results of the presurgical workup.
Adolescent↗
Nonlinear EEG dynamics during sleep in depression and schizophrenia.
The article deals with the question, whether nonlinear analysis of the sleep EEG may give clues to understanding of disturbed information processing in psychiatric diseases. We point out how the nonlinear approach to EEG dynamics is motivated and review recent investigations concerning nonlinear dynamical properties of physiological systems. We present calculations of the correlation dimension D2 and the principal Lyapunov-exponent lambda 1 for sleep EEG data from 9 depressive and 11 schizophrenic inpatients compared to healthy controls. Combining the findings for D2 and lambda 1 our results point to altered nonlinear brain dynamics mainly during slow wave sleep in depression and during REM sleep in schizophrenia. Finally, possible interpretations of altered nonlinear EEG dynamics during sleep concerning disturbed information processing in depression and schizophrenia are discussed.
Adult↗