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At least 973 records · Page 54Linked to original sources

PubMed1995

Endogenous population growth may imply chaos.

The authors consider a discrete-time neoclassical growth model with an endogenous rate of population growth. The resulting one-dimensional map for the capital intensity has a tilted z-shape. Using the theory of nonlinear dynamical systems, they obtain numerical results on the qualitative behavior of time paths for changing parameter values. Besides stable and periodic solutions, erratic time paths may result. In particular, myopic and far-sighted economies--assumed to be characterized by low and high savings rate respectively--are characterized by stable per capita capital stocks, while solutions with chaotic windows exist between these two extremes.

Austria↗

PubMed1991

Self-organized control of bipedal locomotion by neural oscillators in unpredictable environment.

A new principle of sensorimotor control of legged locomotion in an unpredictable environment is proposed on the basis of neurophysiological knowledge and a theory of nonlinear dynamics. Stable and flexible locomotion is realized as a global limit cycle generated by a global entrainment between the rhythmic activities of a nervous system composed of coupled neural oscillators and the rhythmic movements of a musculo-skeletal system including interaction with its environment. Coordinated movements are generated not by slaving to an explicit representation of the precise trajectories of the movement of each part but by dynamic interactions among the nervous system, the musculo-skeletal system and the environment. The performance of a bipedal model based on the above principle was investigated by computer simulation. Walking movements stable to mechanical perturbations and to environmental changes were obtained. Moreover, the model generated not only the walking movement but also the running movement by changing a single parameter nonspecific to the movement. The transitions between the gait patterns occurred with hysteresis.

Animals↗

PubMed1995

Bistability in cerebellar Purkinje cell dendrites modelled with high-threshold calcium and delayed-rectifier potassium channels.

Phase-plane analysis of the ionic currents underlying dendritic plateau potentials was carried out to study the nonlinear dynamics and steady-state transfer properties of the dendritic tree in cerebellar Purkinje cells. The results of an analysis of the P-type calcium and delayed rectifier potassium channel system are presented in this study. These channels constitute a simple system that can support bistability and plateau potentials. By requiring both the steady-state current-voltage curve and nullclines to mimic basic plateau potential properties, we obtained well-defined ranges of specific conductance that can support bistability. Hysteresis was found to be surprisingly prevalent in this simple ion-channel system. Using the steady-state current voltage relationship, we derive concise, algebraic expressions for the voltage and current thresholds of state transitions as functions of specific conductance. The significance of bistability in this ion-channel system is discussed with respect to the generation of plateau potentials in Purkinje cells dendrites and the role of the cerebellum in motor control.

Action Potentials↗

PubMed1995

Nonlinear neuronal mode analysis of action potential encoding in the cockroach tactile spine neuron.

Neuronal mode analysis is a recently developed technique for modelling the behavior of nonlinear systems whose outputs consist of action potentials. The system is modelled as a set of parallel linear filters, or modes, which feed into a multi-input threshold. The characteristics of the principal modes and the multi-input threshold device can be derived from Laguerre function expansions of the computed first- and second-order Volterra kernels when the system is stimulated with a randomly varying input. Neuronal mode analysis was used to model the encoder properties of the cockroach tactile spine neuron, a nonlinear, rapidly adapting, sensory neuron with reliable behavior. The analysis found two principal modes, one rapid and excitatory, the other slower and inhibitory. The two modes have analogies to two of the pathways in a block-structured model of the encoder that was developed from previous physiological investigations of the neuron. These results support the block-structured model and offer a new approach to identifying the components responsible for the nonlinear dynamic properties of this neuronal encoder.

Action Potentials↗

PubMed1995

A model of the neuro-musculo-skeletal system for human locomotion. I. Emergence of basic gait.

The generation of human locomotion was examined by linking computational neuroscience with biomechanics from the perspective of nonlinear dynamical theory. We constructed a model of human locomotion, which includes a musculo-skeletal system with 8 segments and 20 muscles, a neural rhythm generator composed of 7 pairs of neural oscillators, and mechanisms for processing and transporting sensory and motor signals. Using a computer simulation, we found that locomotion emerged as a stable limit cycle that was generated by the global entrainment between the musculo-skeletal system, the neural system, and the environment. Moreover, the walking movements of the model could be compared quantitatively with those of experimental studies in humans.

Biomechanical Phenomena↗

PubMed1993

Deterministic chaos and the first positive Lyapunov exponent: a nonlinear analysis of the human electroencephalogram during sleep.

Under selected conditions, nonlinear dynamical systems, which can be described by deterministic models, are able to generate so-called deterministic chaos. In this case the dynamics show a sensitive dependence on initial conditions, which means that different states of a system, being arbitrarily close initially, will become macroscopically separated for sufficiently long times. In this sense, the unpredictability of the EEG might be a basic phenomenon of its chaotic character. Recent investigations of the dimensionality of EEG attractors in phase space have led to the assumption that the EEG can be regarded as a deterministic process which should not be mistaken for simple noise. The calculation of dimensionality estimates the degrees of freedom of a signal. Nevertheless, it is difficult to decide from this kind of analysis whether a process is quasiperiodic or chaotic. Therefore, we performed a new analysis by calculating the first positive Lyapunov exponent L1 from sleep EEG data. Lyapunov exponents measure the mean exponential expansion or contraction of a flow in phase space. L1 is zero for periodic as well as quasiperiodic processes, but positive in the case of chaotic processes expressing the sensitive dependence on initial conditions. We calculated L1 for sleep EEG segments of 15 healthy men corresponding to the sleep stages I, II, III, IV, and REM (according to Rechtschaffen and Kales). Our investigations support the assumption that EEG signals are neither quasiperiodic waves nor a simple noise. Moreover, we found statistically significant differences between the values of L1 for different sleep stages.(ABSTRACT TRUNCATED AT 250 WORDS)

Adult↗

PubMed1988

Is the normal heart a periodic oscillator?

With the help of several independent methods of nonlinear dynamics, the electrocardiograms (ECG) of four normal human hearts are studied qualitatively and quantitatively. A total of 36 leads were tested. The power spectrum, the autocorrelation function, the phase portrait, the Poincaré section, the correlation dimension, the Lyapunov exponent and the Kolmogorov entropy all point to the fact that the normal heart is not a perfect oscillator. The cardiac activity stems from deterministic dynamics of chaotic nature characterized by correlation dimensions D2 ranging from 3.6 to 5.2. Two different phase spaces are constructed for the evaluation of D2: the introduction of time lags and the direct use of space vectors give similar results. It is shown that the variabilities in interbeat intervals are not random but exhibit short range correlations governed by deterministic laws. These correlations may be related to the accelerating and decelerating physiological processes. This new approach to the cardiac activity may be used in clinical diagnosis. Also they are valuable tools for the evaluation of mathematical models which describe cardiac activity in terms of evolution equations.

Electrocardiography↗

PubMed1990

Phase space topography and the Lyapunov exponent of electrocorticograms in partial seizures.

Electrocorticograms (ECoG's) from 16 of 68 chronically implanted subdural electrodes, placed over the right temporal cortex in a patient with a right medial temporal focus, were analyzed using methods from nonlinear dynamics. A time series provides information about a large number of pertinent variables, which may be used to explore and characterize the system's dynamics. These variables and their evolution in time produce the phase portrait of the system. The phase spaces for each of 16 electrodes were constructed and from these the largest average Lyapunov exponents (L's), measures of chaoticity of the system (the larger the L, the more chaotic the system is), were estimated over time for every electrode before, in and after the epileptic seizure for three seizures of the same patient. The start of the seizure corresponds to a simultaneous drop in L values obtained at the electrodes nearest the focus. L values for the rest of the electrodes follow. The mean values of L for all electrodes in the postictal state are larger than the ones in the preictal state, denoting a more chaotic state postictally. The lowest values of L occur during the seizure but they are still positive denoting the presence of a chaotic attractor. Based on the procedure for the estimation of L we were able to develop a methodology for detecting prominent spikes in the ECoG. These measures (L*) calculated over a period of time (10 minutes before to 10 minutes after the seizure outburst) revealed a remarkable coherence of the abrupt transient drops of L* for the electrodes that showed the initial ictal onset. The L* values for the electrodes away from the focus exhibited less abrupt transient drops. These results indicate that the largest average Lyapunov exponent L can be useful in seizure detection as well as a discriminatory factor for focus localization in multielectrode analysis.

Brain Mapping↗

PubMed1995

Nonlinear analysis of sleep EEG in depression: calculation of the largest lyapunov exponent.

Conventional sleep analysis according to Rechtschaffen and Kales (1968) has provided meaningful contributions to the understanding of disturbed sleep architecture in depression. However, there is no characteristic alteration of the sleep cycle, which could serve as a highly specific feature for depressive illness. Therefore, we started to investigate nonlinear properties of sleep electroencephalographic (EEG) data in order to elucidate functional alterations other than those obtained from classical sleep analysis. The application of methods from nonlinear dynamical system theory to EEG data has led to the assumption that the EEG can be treated as a deterministic chaotic process. Chaotic systems are characterized by a so-called sensitive dependence on initial conditions. This property can be quantified by calculating the system's Lyapunov exponents, which measure the exponential separation of nearby initial states in phase space. For 15 depressive inpatients (major depressive episodes according to DSM-III-R criteria) and 13 healthy controls, matched in gender, age, and education, we computed the principal Lyapunov exponents L1 of EEG segments corresponding to sleep stages, I, II, III, IV, and rapid eye movement (REM), according to Rechtschaffen and Kales, for the lead positions CZ and PZ. We found statistically significant decreased values of L1 during sleep stage IV in depressives compared with a healthy control group.

Adult↗

PubMed2000

Effects of microwave radiation and strychnine on cerebral biopotentials in narcotized rats.

Strychnine and microwave radiation produced changes in spectral parameters of electrocorticogram, correlation dimension, and Kolmogorov entropy, parameters calculated by the methods of nonlinear dynamics opposite to those induced by urethane. The modulatory effect of microwaves on bioelectric cerebral activity in narcotized animals was similar to the effect of strychnine and probably related to enhanced excitability of brain structures and complication of bioelectric processes.

Animals↗

PubMedDate not supplied

Stoichiometric network analysis.

Stoichiometric network analysis is a systematic, general approach to the qualitative, nonlinear dynamics of chemical reaction mechanisms and other systems with stoichiometry. The advantage of a qualitative approach is that no rate constants are needed to determine qualitative features of the dynamics. If one is interested in stability, the approach yields inequalities among the steady-state concentrations and the rate of flow through sequences of important reactions. These parameters are often the ones most easily measured experimentally. By comparing such experiments with the inequalities derived from stoichiometric network analysis, one can often prove that certain mechanisms cannot account for oscillations or other types of observed dynamics. The approach covers far more than stability. The existence of steady states of zero concentration has an interesting mathematics and applies to chemical evolution. The folding of the manifold of steady states can be found by direct calculation and plays a role in switching enzymes on and off. The approach leads to theorems showing that some steady states are globally attracting or, possibly, that a region containing chaos or an oscillation is globally attracting. The subject of sensitivity analysis has been reformulated in this context. Algorithms that apply many of the theoretical results to chemical networks have been developed and combined into a computer program package.

Chemical Phenomena↗

PubMed1999

A continuous, age-structured insect population model.

A continuous age-structured model of cannibalistic insect populations is constructed and analyzed. The model is a continuous analog of the model used in the recent work of Costantino et al. in which discrete modeling, mathematical analysis, statistical techniques, and laboratory experiments were used to demonstrate the presence of nonlinear dynamics, including chaos, in laboratory Tribolium cultures. A special case of the continuous model (no larva-on-egg cannibalism) is analyzed and the results are compared to the analogous special case of the discrete model.

Age Factors↗

PubMed2000

Topographic analysis of dimension estimates of EEG and filtered rhythms in epileptic patients with complex partial seizures.

Nonlinear dynamic properties were analyzed on the EEG and filtered rhythms recorded from healthy subjects and epileptic patients with complex partial seizures. Estimates of correlation dimensions of control EEG, interictal EEG and ictal EEG were calculated. The values were demonstrated on topograms. The delta (0.5-4 Hz), theta (4-8 Hz), alpha (8-13 Hz), beta (13-30 Hz) and gamma (30-40 Hz) components were obtained and considered as signals from the cortex. Corresponding surrogate data was produced. Firstly, the influence of sampling parameters on the calculation was tested. The dimension estimates of the signals from the frontal, temporal, parietal and occipital regions were computed and compared with the results of surrogate data. In the control subjects, the estimates between the EEG and surrogate data did not differ (P > 0.05). The interictal EEG from the frontal region and occipital region, as well as its theta component from the frontal region, and temporal region, showed obviously low dimensions (P < 0.01). The ictal EEG exhibited significantly low-dimension estimates across the scalp. All filtered rhythms from the temporal region yielded lower results than those of the surrogate data (P < 0.01). The dimension estimates of the EEG and filtered components markedly changed when the neurological state varied. For each neurological state, the dimension estimates were not uniform among the EEG and frequency components. The signal with a different frequency range and in a different neurological state showed a different dimension estimate. Furthermore, the theta and alpha components demonstrated the same estimates not only within each neurological state, but also among the different states. These results indicate that the theta and alpha components may be caused by similar dynamic processes. We conclude that the brain function underlying the ictal EEG has a simple mechanism. Several heterogeneous dynamic systems play important roles in the generation of EEG.

Adult↗

PubMed1997

On the correlation dimension of optokinetic nystagmus eye movements: computational parameters, filtering, nonstationarity, and surrogate data.

We discuss the estimation of the correlation dimension of optokinetic nystagmus (OKN), a type of reflexive eye movement. Parameters of the time-delay reconstruction of the attractor are investigated, including the number of data points, the time delay, the window duration, and the duration of the signal being analyzed. Adequate values are recommended. Digital low-pass filtering causes the dimension to increase as the filter cutoff frequency decreases, in accord with a previously published prediction. The stationarity of the correlation dimension is examined; the dimension appears to decrease over the course of 120 s of continuous stimulation. Implications for the reliable estimation of the dimension are considered. Several surrogate data sets are constructed, based on both early (0-30 s) and late (100-130 s) OKN segments. Most of the surrogate data sets randomize some aspect of the original OKN, while maintaining other aspects. Dimensions are found for all surrogates and for the original OKN. Evidence is found that is consistent with some amount of deterministic and nonlinear dynamics in OKN. When this structure is randomized in the surrogate, the dimension changes or the dimension algorithm ceases to converge to a finite value. Implications for further analysis and modeling of OKN are discussed.

Humans↗

PubMed2006

On the advantages of multi-input single-output parallel cascade classifiers.

Parallel Cascade Identification (PCI) has been successfully applied to build dynamic nonlinear systems that address diverse challenges in the field of bioinformatics. PCI may be used to identify either single-input single-output (SISO) or multi-input single-output (MISO) models. Although SISO PCI models have typically sufficed, it has been suggested that MISO PCI systems could also be used to form bioinformatics classifiers, and indeed they were successfully applied in one study. This paper reports on the first systematic comparison of MISO and SISO PCI classifiers. Motivation for using the MISO structure is given. The construction of MISO parallel cascade models is also briefly reviewed. In order to compare the accuracy of SISO and MISO PCI classifiers, genetic algorithms are applied to optimize the model architecture on a number of equivalent single-input and multi-input biological training datasets. Through evaluation of both model structures on independent test datasets, we establish that MISO PCI is capable of building classifiers of equal accuracy to those resulting from SISO PCI models. Moreover, we discuss and illustrate the benefits of the MISO approach, including significant reduction in training and testing times, and the ability to adjust automatically the weighting of individual inputs according to information content.

Algorithms↗

PubMed2007

Estimation and prediction with HIV-treatment interruption data.

We consider longitudinal clinical data for HIV patients undergoing treatment interruptions. We use a nonlinear dynamical mathematical model in attempts to fit individual patient data. A statistically-based censored data method is combined with inverse problem techniques to estimate dynamic parameters. The predictive capabilities of this approach are demonstrated by comparing simulations based on estimation of parameters using only half of the longitudinal observations to the full longitudinal data sets.

Antiretroviral Therapy, Highly Active↗

PubMed2002

Heart rate variability and cardiovascular mortality.

The autonomic nervous system plays a major role in affecting the cardiac milieu and promoting malignant ventricular activity. The measurement of heart rate variability (HRV) is a noninvasive tool for assessing the status of the autonomic nervous system. A depressed HRV among post-myocardial infarction patients is a well-established risk factor for arrhythmic death. A reduced HRV has also been used to identify diabetic patients with autonomic neuropathy. This paper presents recent developments in the use of HRV, focusing on further refinement and validation of the use of both linear and nonlinear dynamics for sudden death prognostication, evaluation of the effect of specific pharmacologic agents on HRV, and assessment of HRV in health and in specific disease states that have been associated with an increased mortality risk.

Autonomic Nervous System↗

PubMed1989

Catastrophe modeling of the accident process: evaluation of an accident reduction program using the occupational hazards survey.

The report details a catastrophe theory model of the accident process with empirical validation. According to the cusp model, two distinct levels of risk can be observed for a distribution of group accident rates, one at 0.0 Occupational Safety and Health Association (OSHA)-reportable accidents per 100 person-years of exposure and one at 11.5. Changes within or between the two levels are determined by two control parameters: environmental hazard (asymmetry) and operator load (bifurcation). The sample consisted of 68 work groups from 8 Milwaukee-Chicago area sheet metal mills and foundries who completed the Occupational Hazards Survey (OHS). The OHS contributed six bifurcation variables (safety management, life stress, physical stress anxiety, beliefs about accident control, and experience) and two asymmetry variables (environmental hazards and danger). All organizations received an interpretive report of their survey responses with recommendations for accident control, and had held their reports for two to nine months at the time the follow-up accident rate data were collected. There were two additional bifurcation variables: months holding report and group size. Regression analysis determined that the cusp model (R2 = .42) was more than twice as accurate as the best log-linear or linear alternative. Accidents were successfully controlled by safety managers' attention to recommendations produced by the OHS analysis. Catastrophe theory provided some novel insights regarding the linkage between predictor variables and actual behavior. Research has shown that a substantial percentage of occupational accidents are the result of human error. In an effort to explain and predict such errors in a systematic manner, an accident process model based on the cusp catastrophe is developed and tested. The model offers several unique and useful properties: (1) It proposes that changes in accident rates for work groups are the result of a nonlinear dynamic process. (2) The distribution of accident rates is bimodal, with one model near zero and the other at some higher level. (3) Changes in accident rates are predicted from four sources: (i) ambient danger and hazard levels, (ii) variables that impact upon human performance capability, (iii) initial accident rates, and (iv) the mathematical function that interrelates those variables. (4) The mathematical model has inherent properties that allow for causal inference. Environmental and human performance factors can be operationalized as sets of more specific variables. In this application. The Occupational Hazards Survey was used to gather data from mill and foundry workers pertaining to hazards and dangers, adequacy of safety management, stress, anxiety, and beliefs about accident control.(ABSTRACT TRUNCATED AT 400 WORDS)

Accident Prevention↗