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At least 1,621 records · Page 90Linked to original sources
PubMed2005

Hysteresis dynamics, bursting oscillations and evolution to chaotic regimes.

This article describes new aspects of hysteresis dynamics which have been uncovered through computer experiments. There are several motivations to be interested in fast-slow dynamics. For instance, many physiological or biological systems display different time scales. The bursting oscillations which can be observed in neurons, beta-cells of the pancreas and population dynamics are essentially studied via bifurcation theory and analysis of fast-slow systems (Keener and Sneyd, 1998; Rinzel, 1987). Hysteresis is a possible mechanism to generate bursting oscillations. A first part of this article presents the computer techniques (the dotted-phase portrait, the bifurcation of the fast dynamics and the wave form) we have used to represent several patterns specific to hysteresis dynamics. This framework yields a natural generalization to the notion of bursting oscillations where, for instance, the active phase is chaotic and alternates with a quiescent phase. In a second part of the article, we emphasize the evolution to chaos which is often associated with bursting oscillations on the specific example of the Hindmarsh-Rose system. This evolution to chaos has already been studied with classical tools of dynamical systems but we give here numerical evidence on hysteresis dynamics and on some aspects of the wave form. The analytical proofs will be given elsewhere.

Islets of Langerhans↗
PubMed1998

Viscoelastic constitutive law in large deformations: application to human knee ligaments and tendons.

Traction tests on soft tissues show that the shape of the stress strain curves depends on the strain rate at which the tests are performed. Many of the constitutive models that have been proposed fail to properly consider the effect of the strain rate when large deformations are encountered. In the present study, a framework based on elastic and viscous potentials is developed. The resulting constitutive law is valid for large deformations and satisfies the principles of thermodynamics. Three parameters -- two for the elasticity and one for the viscosity -- were enough to precisely fit the non-linear stress strain curves obtained at different strain rates with human cruciate ligaments and patellar tendons. The identification results then in a realistic, three-dimensional viscoelastic constitutive law. The developed constitutive law can be used regardless of the strain or rotation values. It can be incorporated into a finite element program to model the viscoelastic behavior of ligaments and tendons under dynamic situations.

Algorithms↗
PubMed2001

Effect of trends on detrended fluctuation analysis.

Detrended fluctuation analysis (DFA) is a scaling analysis method used to estimate long-range power-law correlation exponents in noisy signals. Many noisy signals in real systems display trends, so that the scaling results obtained from the DFA method become difficult to analyze. We systematically study the effects of three types of trends--linear, periodic, and power-law trends, and offer examples where these trends are likely to occur in real data. We compare the difference between the scaling results for artificially generated correlated noise and correlated noise with a trend, and study how trends lead to the appearance of crossovers in the scaling behavior. We find that crossovers result from the competition between the scaling of the noise and the "apparent" scaling of the trend. We study how the characteristics of these crossovers depend on (i) the slope of the linear trend; (ii) the amplitude and period of the periodic trend; (iii) the amplitude and power of the power-law trend, and (iv) the length as well as the correlation properties of the noise. Surprisingly, we find that the crossovers in the scaling of noisy signals with trends also follow scaling laws--i.e., long-range power-law dependence of the position of the crossover on the parameters of the trends. We show that the DFA result of noise with a trend can be exactly determined by the superposition of the separate results of the DFA on the noise and on the trend, assuming that the noise and the trend are not correlated. If this superposition rule is not followed, this is an indication that the noise and the superposed trend are not independent, so that removing the trend could lead to changes in the correlation properties of the noise. In addition, we show how to use DFA appropriately to minimize the effects of trends, how to recognize if a crossover indicates indeed a transition from one type to a different type of underlying correlation, or if the crossover is due to a trend without any transition in the dynamical properties of the noise.

Analysis of Variance↗
PubMed2001

Regularization of synchronized chaotic bursts.

The onset of regular bursts in a group of irregularly bursting neurons with different individual properties is one of the most interesting dynamical properties found in neurobiological systems. In this paper we show how synchronization among chaotically bursting cells can lead to the onset of regular bursting. In order to clearly present the mechanism behind such regularization we model the individual dynamics of each cell with a simple two-dimensional map that produces chaotic bursting behavior similar to biological neurons.

Animals↗
PubMed2006

Transient and steady-state dynamics of cortical adaptation.

Adaptation is a ubiquitous property of all sensory pathways of the brain and thus likely critical in the encoding of behaviorally relevant sensory information. Despite evidence identifying specific biophysical mechanisms contributing to sensory adaptation, its functional role in sensory encoding is not well understood, particularly in the natural environment where transient rather than steady-state activity could dominate the neuronal representation. Here, we show that the heterogeneous transient and steady-state adaptation dynamics of single cortical neurons in the rat vibrissa system were well characterized by an underlying state variable. The state was directly predictable from temporal response properties that capture the time course of postexcitatory suppression following an isolated vibrissa deflection. Altering the initial state, by preceding the periodic stimulus with an additional vibrissa deflection, strongly influenced single-cell transient cortical adaptation responses. Despite the different transient activity, neurons reached the same steady-state adapted response with a time to steady state that was independent of the initial state. However, the differences in transient activity observed on small time scales were not present when activity was integrated over the longer time scale of a stimulus cycle. Taken together, the results here demonstrate that although adaptation can have significant effects on transient neuronal activity and direction selectivity, a simple measure of the time course of suppression following an isolated stimulus predicted a large portion of the observed adaptation dynamics.

Action Potentials↗
PubMed1999

Effects of alcohol use and gender on the dynamics of EKG time-series data.

Hurst analysis of EKG data obtained from a population of alcoholic (n = 13) and nonalcoholic (n = 48) subjects was undertaken. Potential subjects (n = 120) were screened using the Schedule for Affective Disorders and Schizophrenia and Structured Clinical Interview for DSM-III instruments. Data from subjects with a diagnosis of current alcohol dependence were analyzed. Subjects with diagnoses such as major depression, bipolar disorder or schizophrenia (Axis I diagnoses), or personality disorders (Axis II diagnoses) were excluded from analysis. Subjects undergoing testing were free of alcohol and illicit drugs. Alcoholic subjects had no clinical evidence of alcohol withdrawal symptoms at the time of testing. EKG data were obtained with eyes open or with eyes closed. Approximately 3.5 min of data were obtained for each condition. Alcoholic subjects had less complex heart rate dynamics as evidenced by higher values of H = 0.18 +/- 0.05 (mean +/- SEM), compared with healthy comparison subjects with H = 0.09 +/- 0.02, p < 0.014 for the eyes closed condition, and H = 0.17 +/- 0.05 (mean +/- SEM) compared with healthy comparison subjects with H = 0.07 +/- 0.02,p < 0.011 for the eyes open condition. A gender effect was seen, with female subjects showing evidence of more complex heart rate dynamics than male subjects.

Alcohol Drinking↗
PubMed1995

Normal pressure hydrocephalus: an analysis of aetiology and response to shunting based on mathematical modeling.

The dynamics which maintain the state of enlarged cerebral ventricles and normal intracranial pressures (normal pressure hydrocephalus) are not completely understood, making the response to cerebrospinal fluid diversion difficult to predict. Using our previously described mathematical model of intracranial physiology which allows nonlinear relationships of pressure, volume, and flow in 7 distinct compartments, we desired to determine factors which could be responsible for the development and maintenance of the steady state of normal pressure hydrocephalus. Using typical starting values for CSF volume, pressure, and flow, the model indicates that this condition cannot be sustained, in spite of high CSF outflow resistance, unless capillary flow resistance is elevated. This condition can be the result of arterial hypertension. The additional modeling of a CSF diversion device demonstrates predicted time courses for ventricular size reduction which are consistent with clinical observations. We conclude that certain vascular conditions may allow for the maintenance of an enlarged ventricular size, and that mathematical modeling can assist in identifying factors for clinical study that may maintain normal pressure hydrocephalus even after treatment by CSF diversion.

Cerebral Ventricles↗
PubMed2002

Influence of atropine on fractal and complexity measures of heart rate variability.

BACKGROUND: Measurement of short-term fractal-like correlation properties of heart rate dynamics has been shown to be a useful prognostic indicator of adverse events in cardiac patients. Complexity measurements of heart rate variability (HRV) have already provided important information in many cardiac conditions. However, data on the physiological background of these newer nonlinear measures of HRV are limited. METHODS: Nine healthy subjects (aged from 22 to 35 years, 6 males, 3 females) had an electrocardiographic (ECG) recording during controlled breathing in supine position. HRV was analyzed for 5 min periods before and after intravenous injection of 0.6 mg of atropine using conventional HRV measures and newer nonlinear HRV measures including the short-term scaling exponent (alpha(1)) and approximate entropy (ApEn). RESULTS: The short-term scaling exponent alpha(1) increased significantly after atropine injection (1.01 +/- 0.23 vs 1.43 +/- 0.19, P = 0.001). There was no significant difference between ApEn values before and after atropine injection (0.87 +/- 0.17 vs 0.70 +/- 0.31, respectively, P = 0.27). At baseline before atropine administration, alpha(1) had a significant negative correlation with SDNN, RMSSD, and HF (r = -0.70, -0.76, -0.67, respectively, P < 0.05 for all), and a significant positive correlation with heart rate (r = 0.76, P < 0.05). After atropine injection, alpha(1) did not have significant correlation with any of the HRV parameters or heart rate. There were no significant correlations between ApEn and any of the HRV measures or heart rate either before or after atropine administration. CONCLUSIONS: Vagal tone has an important influence on the values of the short-term scaling exponent alpha(1). However, vagal modulation is not a major determinant of the values of ApEn.

Adult↗
PubMed2002

Does preprocessing change nonlinear measures of heart rate variability?

This work investigated if methods used to produce a uniformly sampled heart rate variability (HRV) time series significantly change the deterministic signature underlying the dynamics of such signals and some nonlinear measures of HRV. Two methods of preprocessing were used: the convolution of inverse interval function values with a rectangular window and the cubic polynomial interpolation. The HRV time series were obtained from 33 Wistar rats submitted to autonomic blockade protocols and from 17 healthy adults. The analysis of determinism was carried out by the method of surrogate data sets and nonlinear autoregressive moving average modelling and prediction. The scaling exponents alpha, alpha(1) and alpha(2) derived from the detrended fluctuation analysis were calculated from raw HRV time series and respective preprocessed signals. It was shown that the technique of cubic interpolation of HRV time series did not significantly change any nonlinear characteristic studied in this work, while the method of convolution only affected the alpha(1) index. The results suggested that preprocessed time series may be used to study HRV in the field of nonlinear dynamics.

Adolescent↗
PubMedDate not supplied

Fractal dynamics of heart beat interval fluctuations in corticotropin-releasing factor receptor subtype 2 deficient mice.

Non-linear fractal analysis of cardiac interbeat time series was performed in corticotropin-releasing factor receptor subtype 2 (CRFR2) deficient mice. Heart rate dynamics in mice constitutes a self-similar, scale-invariant, random fractal process with persistent intrinsic long-range correlations and inverse power-law properties. We hypothesized that the sustained tachycardic response elicited by intraperitoneal (ip) injection of human/rat CRF (h/rCRF) is mediated by CRFR2. In wildtype control animals, heart rate was increased to about maximum levels (approximately 750 bpm) while in CRFR2-deficient animals baseline values were retained (approximately 580 bpm). The tachycardic response elicited by ip-application is mediated by CRFR2 and is interpreted to result from sympathetic stimulation. However, the functional integrity of CRFR2 would not present a prerequisite to maintaining the responsiveness and resiliency of cardiac control to external environmental perturbations experimentally induced by extrinsic ip-application of h/rCRF or under physiological conditions that may be associated with an increased peripheral release of CRF. Under stressful physiological conditions achieved by novelty exposure, CRFR2 is not involved in the cardiodynamic regulation to external short-term stress. While the hypothesis of involvement of CRFR2 in cardiac regulation upon pharmacological stimulation cannot be rejected, the present findings suggest that the mechanism of action is by sympathetic stimulation, but would not unambiguously allow to draw any conclusions as to the physiological role of CRFR2 in the control of cardiac dynamics.

Adrenergic beta-Antagonists↗
PubMed2006

Early motor development from partially ordered neural-body dynamics: experiments with a cortico-spinal-musculo-skeletal model.

Early human motor development has the nature of spontaneous exploration and boot-strap learning, leading to open-ended acquisition of versatile flexible motor skills. Since dexterous motor skills often exploit body-environment dynamics, we formulate the developmental principle as the spontaneous exploration of consistent dynamical patterns of the neural-body-environment system. We propose that partially ordered dynamical patterns emergent from chaotic oscillators coupled through embodiment serve as the core driving mechanism of such exploration. A model of neuro-musculo-skeletal system is constructed capturing essential features of biological systems. It consists of a skeleton, muscles, spindles, tendon organs, spinal circuits, medullar circuits (CPGs), and a basic cortical model. Through a series of experiments with a minimally simple body model, it is shown that the model has the capability of generating partially ordered behavior, a mixture of chaotic exploration and ordered entrained patterns. Models of self-organizing cortical areas for primary somatosensory and motor areas are introduced. They participate in the explorative learning by simultaneously learning and controlling the movement patterns. A scaled up version of the model, a human infant model, is constructed and put through preliminary experiments. Some meaningful motor behavior emerged including rolling over and crawling-like motion. The results show the possibility that a rich variety of meaningful behavior can be discovered and acquired by the neural-body dynamics without pre-defined coordinated control circuits.

Behavior↗
PubMed1999

Investigation of the dynamics underlying periodic complexes in the EEG.

Periodic complexes (PC), occurring lateralised or diffuse, are relatively rare EEG phenomena which reflect acute severe brain disease. The pathophysiology is still incompletely understood. One hypothesis suggested by the alpha rhythm model of Lopes da Silva is that periodic complexes reflect limit cycle dynamics of cortical networks caused by excessive excitatory feedback. We examined this hypothesis by applying a recently developed technique to EEGs displaying periodic complexes and to periodic complexes generated by the model. The technique, non-linear cross prediction, characterises how well a time series can be predicted, and how much amplitude and time asymmetry is present. Amplitude and time asymmetry are indications of non-linearity. In accordance with the model, most EEG channels with PC showed clear evidence of amplitude and time asymmetry, pointing to non-linear dynamics. However, the non-linear predictability of true PC was substantially lower than that of PC generated by the model. Furthermore, no finite value for the correlation dimension could be obtained for the real EEG data, whereas the model time series had a dimension slighter higher than one, consistent with a limit cycle attractor. Thus we can conclude that PC reflect non-linear dynamics, but a limit cycle attractor is too simple an explanation. The possibility of more complex (high dimensional and spatio-temporal) non-linear dynamics should be investigated.

Acute Disease↗
PubMed1995

Chaos: a potential problem in the biological control of insect pests.

Erratic variations are normally observed in the populations of insect pests that destroy crop plants. To establish a scientific basis for developing effective control procedures, we have developed a model system for the European Corn Borer (ECB) (Ostrinia nubilalis) for which extensive field data, as well as laboratory results, have been accumulated during the past four decades. The model includes both a natural ECB pathogen and a genetically engineered toxin-producing agent as possible means of biological control. Our aim was to determine the conditions that could cause the population to vary erratically, as observed in the field. The erratic behavior in our simulations was analyzed to determine whether it is chaotic; chaos is a distinct type of erratic behavior which shows extreme sensitivity to initial conditions, i.e., the starting size of the population. Our simulations show that an increase in the death rate of the infected ECB, or a decrease in the birth rate of uninfected ECBs from infected ones, variables that are known to be affected by weather conditions, can induce a chaotic regime in which ECB population peaks reach values far higher than before chaos set in. Population peaks are even greater in the presence of both biological control agents. The results show that a biological control regime cannot be effective under conditions that induce chaotic population dynamics. Microcosm studies could be used to determine whether this situation would occur in the field.

Animals↗
PubMed2006

Amplitude and phase dynamics associated with acoustically paced finger tapping.

To gain insight into the brain activity associated with the performance of an acoustically paced synchronization task, we analyzed the amplitude and phase dynamics inherent in magnetoencephalographic (MEG) signals across frequency bands in order to discriminate between evoked and induced responses. MEG signals were averaged with respect to motor and auditory events (tap and tone onsets). Principal component analysis was used to compare amplitude and phase changes during listening and during paced and unpaced tapping, allowing a separation of brain activity related to motor and auditory processes, respectively. Motor performance was accompanied by phasic amplitude changes and increased phase locking in the beta band. Auditory processing of acoustic stimuli resulted in a simultaneous increase of amplitude and phase locking in the theta and alpha band. The temporal overlap of auditory-related amplitude changes and phase locking indicated an evoked response, in accordance with previous studies on auditory perception. The temporal difference of movement-related amplitude and phase dynamics in the beta band, on the other hand, suggested a change in ongoing brain activity, i.e., an induced response supporting previous results on motor-related brain dynamics in the beta band.

Acoustic Stimulation↗
PubMed2004

Using a quantitative blueprint to reprogram the dynamics of the flagella gene network.

Detailed understanding and control of biological networks will require a level of description similar to that of electronic engineering blueprints. Currently, however, even the best-studied systems are usually described using qualitative arrow diagrams. A quantitative blueprint requires in vivo measurements of (1) the relative strength of the interactions (numbers on the arrows) and (2) the functions that integrate multiple inputs. Here, we address this using a well-studied system, the flagella biosynthesis transcription network in Escherichia coli. We use theory and high-resolution experiments to obtain a quantitative blueprint with (1) numbers on the arrows, finding different hierarchies of activation coefficients for the two regulators, FlhDC and FliA; and (2) cis-regulatory input functions, which summate the input from the two regulators (SUM gates). We then demonstrate experimentally how this blueprint can be used to reprogram temporal expression patterns in this system, using controlled expression of the regulators or point mutations in their binding sites. The present approach can be used to define blueprints of other gene networks and to quantitatively reprogram their dynamics.

Algorithms↗
PubMed1994

Role of chaotic dynamics in neural plasticity.

Mathematical models are essential for the study of complex neural systems at all levels of the hierarchy from macromolecules through neurons to brain systems. ANN are readily available, but most of them are inappropriate for modeling brain function in normal behavior, because they stem from studies of neural systems in anesthetized or paralyzed animals which are capable only of reflux output. That class of models lacks the goal-directed, self-organizing properties of neural systems in behaving animals. In contrast to the stability of ANN and their reliance on asymptotic convergence to steady states (point attractors) and periodic oscillations (limit cycle attractors), BNN are intrinsically unstable. They continuously generate 'spontaneous' aperiodic activity that manifests the operation of chaotic dynamics undergoing repeated state transitions. Observations on the activity patterns of sensory cortex reveal that the perceptual outputs of BNN are by construction of spatial patterns and dynamic trajectories and not by computation using symbolic representations. Chaotic dynamics plays essential roles both in the construction of perceptions and in the continuing update of cortical populations, which requires selective synaptic modification during associative learning and habituation. Simultaneous multichannel recording from the olfactory bulb and cortex has given the following experimental results. (1) The cortical activity that relates to the perception of a sensory stimulus is carried macroscopically by a smaller number of single neurons e.g. 'units', 'feature detectors'. (2) The macroscopic activity reflects the meaning and significance of the stimulus for the experimental subject and not the stimulus as it is known to the observer. (3) The activity carries the meaning in spatial patterns, not in time series (the difference between a phonograph or radio and movie or TV). (4) The spatial patterns of activity that accompany previously learned stimuli or responses are changed by the introduction of new stimuli and also by modifications in reinforcement contingencies. There is no invariance in the memory store within the populations. (5) The patterns of activity are created by dynamic neural interactions in sensory cortex, not by registration or filtering of stimuli. There is no evidence for storage, retrieval, cross-correlation or logical tree search. (6) The dynamics is chaotic, not merely noisy, so that each act of perception involves a new construction by the cortex not by mere information processing. From these findings we infer that chaotic dynamics plays a crucial role in the construction of the associational contexts comprising the memory systems of experimental subjects.

Animals↗
PubMed1997

EEG alpha dynamics as viewed from EEG dimension dynamics.

EEG alpha power covaries with changes in visual input and with changes in other aspects of cortical processing. We present an synopsis of three experiments that demonstrate these effects. A concurrent analysis of the EEG dimension indicates that the dynamics of EEG alpha may result from at least two different mechanisms.

Adolescent↗
PubMed2001

Reconstruction of chaotic dynamics by on-line EM algorithm.

In this paper, we discuss the reconstruction of chaotic dynamics by using a normalized Gaussian network (NGnet), which is a network of local linear regression units. The NGnet is trained by an on-line EM algorithm in order to learn the vector field of the chaotic dynamics. We investigate the robustness of our approach to two kinds of noise processes: system noise and observation noise. System noise disturbs the system dynamics itself. Observation noise is added when the state variables are observed. It is shown that the trained NGnet is able to reproduce a chaotic attractor, which approximates the complexity and instability of the original chaotic attractor well, even under various noise conditions. The trained NGnet also shows good prediction performance. When only part of the dynamical variables are observed, the delay embedding method is used. The NGnet is then trained to learn the vector field in the delay coordinate space. Experiments show that the chaotic dynamics embedded in the delay coordinate space is able to be learned under the two types of noise.

Algorithms↗