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PubMed2000

Chaotic behavior of renal sympathetic nerve activity: effect of baroreceptor denervation and cardiac failure.

Nonlinear dynamic analysis was used to examine the chaotic behavior of renal sympathetic nerve activity in conscious rats subjected to either complete baroreceptor denervation (sinoaortic and cardiac baroreceptor denervation) or induction of congestive heart failure (CHF). The peak interval sequence of synchronized renal sympathetic nerve discharge was extracted and used for analysis. In control rats, this yielded a system whose correlation dimension converged to a low value over the embedding dimension range of 10-15 and whose greatest Lyapunov exponent was positive. Complete baroreceptor denervation was associated with a decrease in the correlation dimension of the system (before 2.65 +/- 0.27, after 1.64 +/- 0.17; P < 0.01) and a reduction in chaotic behavior (greatest Lyapunov exponent: 0.201 +/- 0.008 bits/data point before, 0.177 +/- 0.004 bits/data point after, P < 0.02). CHF, a state characterized by impaired sinoaortic and cardiac baroreceptor regulation of renal sympathetic nerve activity, was associated with a similar decrease in the correlation dimension (control 3.41 +/- 0.23, CHF 2.62 +/- 0.26; P < 0.01) and a reduction in chaotic behavior (greatest Lyapunov exponent: 0.205 +/- 0.048 bits/data point control, 0.136 +/- 0.033 bits/data point CHF, P < 0.02). These results indicate that removal of sinoaortic and cardiac baroreceptor regulation of renal sympathetic nerve activity, occurring either physiologically or pathophysiologically, is associated with a decrease in the correlation dimensions of the system and a reduction in chaotic behavior.

Animals↗

PubMed1998

Acidic deposition, plant pests, and the fate of forest ecosystems.

We present and analyze a nonlinear dynamical system modelling forest-pests interactions and the way they are affected by acidic deposition. The model includes mechanisms of carbon and nitrogen exchange between soil and vegetation, biomass decomposition and microbial mineralization, and defoliation by pest grazers, which are partially controlled by avian or mammalian predators. Acidic deposition is assumed to directly damage vegetation, to decrease soil pH, which in turn damages roots and inhibits microbial activity, and to predispose trees to increased pest attack. All the model parameters are set to realistic values except the inflow of protons to soil and the predation mortality inflicted to the pest which are allowed to vary inside reasonable ranges. A numerical bifurcation analysis with respect to these two parameters is carried out. Five functioning modes are uncovered: (i) pest-free equilibrium; (ii) pest persisting at endemic equilibrium; (iii) forest-pest permanent oscillations; (iv) bistable behavior with the system converging either to pest-free equilibrium or endemic pest presence in accordance with initial conditions; (v) bistable behavior with convergence to endemic pest presence or permanent oscillations depending on initial conditions. Catastrophic bifurcations between the different behavior modes are possible, provided the abundance of predators is not too small. Numerical simulation shows that increasing acidic load can lead the forest to collapse in a short time period without important warning signals.

Acid Rain↗

PubMed1993

Chaos theory applied to the caloric response of the vestibular system.

Developments in the field of nonlinear dynamics has given us a new conceptual framework for understanding the mechanisms involved in the regulation of complex nonlinear systems. This concept, called "chaos" or "deterministic chaos," has been applied to EKG, EEG, and other physiological signals, but not yet to the ENG signal. The underlying geometrical structure in chaotic dynamics is fractal (noninteger dimension), and calculating the fractal dimension of the electronystagmographic recording from caloric testing gave a dimension ranging from 3.3 to 7.7. This result demonstrates that the multidimensional vestibular system, with its numerous neurological pathways, can somehow reduce the degrees of freedom and give rise to an irregular dynamic low-dimensional behavior, which is associated with deterministic chaos.

Caloric Tests↗

PubMed2006

The chaotic nature of temper in humans: a long short-term memory recurrent neural network model.

In mathematics and physics, chaos theory deals with the behavior of certain nonlinear dynamical systems that under certain conditions exhibit a phenomenon known as chaos, which is characterised by a sensitivity to initial conditions. Mathematicians paradoxically call such states of order chaos and distinguish them from randomness. New models for describing and predicting different aspects of behavior are being created which once seemed unpredictable. This is done by focusing on the overall patterns of behavior, showing how stable or unstable they are and identifying the circumstances that make them change. In this paper, we indicate why human temper and mood changes have a chaotic nature. Then, we develop a chaotic model based on a long short-term memory recurrent neural network with irregular embeddings derived by the gamma test to model temper tantrum. We finally use a feedback delay controller to stabilize its chaotic behavior, because it is a plausible method for stabilizing biological neural systems. A lot of aspects of this model are analogous to the human counterpart. The model might suggest, for example, that if a particular person had stronger ego defenses, and attended a little less vigilantly to the external world, he or she might find a stable attractor amidst of a broader landscape of chaotic attractors. A therapist or self-control would be analogous to the delayed feedback controller, by specifically encouraging those changes, he might help the person reach a stable behavior. Finally, some comments are proposed to facilitate the normal behavior.

Computer Simulation↗

PubMed1994

Time dependencies in the occurrences of epileptic seizures.

A new method of analysis, developed within the framework of nonlinear dynamics, is applied to patient recorded time series of the occurrence of epileptic seizures. These data exhibit broad band spectra and generally have no obvious structure. The goal is to detect hidden internal dependencies in the data without making any restrictive assumptions, such as linearity, about the structure of the underlying system. The basis of our approach is a conditional probabilistic analysis in a phase space reconstructed from the original data. The data, recorded from patients with intractable epilepsy over a period of 1-3 years, consist of the times of occurrences of hundreds of partial complex seizures. Although the epileptic events appear to occur independently, we show that the epileptic process is not consistent with the rules of a homogeneous Poisson process or generally with a random (IID) process. More specifically, our analysis reveals dependencies of the occurrence of seizures on the occurrence of preceding seizures. These dependencies can be detected in the interseizure interval data sets as well as in the rate of seizures per time period. We modeled patient's inaccuracy in recording seizure events by the addition of uniform white noise and found that the detected dependencies are persistent after addition of noise with standard deviation as great as 1/3 of the standard deviation of the original data set. A linear autoregressive analysis fails to capture these dependencies or produces spurious ones in most of the cases.

Adult↗

PubMed2003

Self-regulation phenomena applied to bacterial reaction centers: 2. Nonequilibrium adiabatic potential: dark and light conformations revisited.

Experimental and theoretical results in support of nonlinear dynamic behavior of photosynthetic reaction centers under light-activated conditions are presented. Different conditions of light adaptation allow for preparation of reaction centers in either of two different conformational states. These states were detected both by short actinic flashes and by the switching of the actinic illumination level between different stationary state values. In the second method, the equilibration kinetics of reaction centers isolated from Rhodobacter sphaeroides were shown to be inherently biphasic. The fast and slow equilibration kinetics are shown to correspond to electron transfer (charge separation) at a fixed structure and to combined electron-conformational transitions governed by the bounded diffusion along the potential surface, respectively. The primary donor recovery kinetics after an actinic flash revealed a pronounced dependence on the time interval (deltat) between cessation of a lengthy preillumination of a sample and the actinic flash. A pronounced slow relaxation component with a decay half time of more than 50 s was measured for deltat > 10 s. This component corresponds to charge recombination in reaction centers for which light-induced structural changes have not relaxed completely before the flash. The amplitude of this component depended on the conditions of the sample preparation, specifically on the type of detergent used in the preparation. The redox potential parameters as well as the structural diffusion constants were estimated for samples prepared in different ways.

Adaptation, Physiological↗

PubMed2001

Normalized entropy applied to the analysis of interindividual and gender-related differences in the cardiovascular effects of stress.

Nonlinear dynamic methods are considered to be a potential tool for studying the complex behavior of the cardiovascular system. In the present study, interindividual and gender-related differences in cardiovascular (CV) responses to various stress stimuli were studied using conventional CV variables such as heart rate (HR) and blood pressure (BP), as well as a recently introduced criterion of system complexity, normalized entropy (E/H, where E is entropy and H is system energy). A group of healthy students (n = 270) of both genders (17-20 years of age) were subjected to noise exposure, mental arithmetic, arithmetic against noise and examination stress. Results showed that CV reactivity depended upon the kind of stress imposed and the gender of the subject. HR and BP stress-induced responses did not differ between men and women. However, men had higher absolute BP levels at baseline and during exposure to stressors. Stress-induced pressor responses lasted longer in men than in women. Changes in the complexity degree of CV signals, as assessed by E/H, were more pronounced and prolonged than those of HR and BP. Unlike the latter, E/H changed significantly in all stress situations for each subject tested and could be divided into two types of stress-induced response. These results allow one to conclude that E/H can better quantitate individual differences in CV stress reactivity in comparison with HR and BP. These findings suggest that stress-induced changes in CV functioning are more varied than can be revealed by applying conventional CV measures.

Adolescent↗

PubMedDate not supplied

Chaotic analysis of electromyography signal at low back and lower limb muscles during forward bending posture.

The present study aims to perform further investigation on muscular activity during forward bending posture by applying a nonlinear dynamic (chaotic) analysis method. The objective is to determine the characteristics of the low back and lower limb muscle electromyography (EMG) signal under chaotic analysis while maintaining a certain posture. Twelve subjects were asked to maintain postures of six stages in bending angles from 0 to 180 degrees, and the EMG signals of erector spinae (ES) at L1 and L5 levels, hamstrings, and gastrocnemius were recorded. Two important concepts to characterize deterministic chaos, Correlation Dimension (D2) and Lyapunov Exponents (lambda, LE), were applied to observe the chaotic characteristic of the EMG signals, and the results were also compared to the FFT based total power value. The EMG signals in all observed muscles during bending posture showed results of positive LE and high D2 at 5.5 to 7.5, which led us to classify EMG as a high dimension chaotic signal. The result obtained showed that the correlation dimension could be used as a reliable method to compare the EMG signal in various postures (or muscle contraction conditions). However, Lyapunov exponents did not show a significant difference of comparison result thus leading to the conclusion that LE could not be a reliable measure for high dimension chaotic system, such as an EMG signal. It was also shown that in both light and deep bending, the EMG signal of the low back muscles was of the same complexity level due to the D2 result. It was evident that somehow the low back muscle remained loaded in all bending stages which was contrary to the hypothesis that the low back muscle was less active during the deep bending, as was the case in most of the previous studies. The reason of such phenomenon was elucidated with use of the theory of muscular functional differentiation, including corticalization and spinalization.

Adult↗

PubMed2002

Global quantitative predictions of complex laser dynamics.

We demonstrate unprecedented agreement between a theoretical two-dimensional bifurcation diagram and the corresponding experimental stability map of an optically injected semiconductor laser over a large range of relevant injection parameter values. The bifurcation diagram encompasses both local and global bifurcations mapping out regions of regular, chaotic, and multistable behavior in considerable detail. This demonstrates the power of dynamical systems modeling for the quantitative prediction of nonlinear dynamics and chaos of semiconductor lasers.

Journal Article↗

PubMed2005

Estimating phase synchronization in dynamical systems using cellular nonlinear networks.

We propose a method for estimating phase synchronization between time series using the parallel computing architecture of cellular nonlinear networks (CNN's). Applying this method to time series of coupled nonlinear model systems and to electroencephalographic time series from epilepsy patients, we show that an accurate approximation of the mean phase coherence R--a bivariate measure for phase synchronization--can be achieved with CNN's using polynomial-type templates.

Action Potentials↗

PubMed2002

Enhancement of phase clustering in the EEG/MEG gamma frequency band anticipates transitions to paroxysmal epileptiform activity in epileptic patients with known visual sensitivity.

A new analytical method for quantifying brain activity from magnetoelectroencephalogram (MEG) and electroencephalogram (EEG) recordings during periodic light stimulation is proposed. It consists in estimating the phase clustering of harmonically related frequency components of a subject's MEG/EEG responses evoked by the light stimulation. The method was developed to test the hypothesis that changes in the dynamics of brain systems in the course of intermittent photic stimulation (IPS) may precede the transition to seizure activity in photosensitive patients. We assumed that such changes would be reflected in the phase of harmonic components of the evoked responses. Thus, we determined the phase clustering for different harmonic components of these MEG/EEG signals. We found that the patients who develop epileptiform discharges during IPS present an enhancement of the phase clustering index at the gamma frequency band, compared with that at the driving frequency. We introduce a quantity--relative phase clustering index (rPCI)--by means of which this enhancement can be quantified. We argue that this quantity reflects the degree of excitability of the underlying dynamical system and it can indicate presence of nonlinear dynamics. rPCI can be applied to detect transitions to epileptic seizure activity in patients with known sensitivity to IPS.

Brain Mapping↗

PubMed2003

Modeling of finite amplitude acoustic waves in closed cavities using the Galerkin method.

Nonlinear resonant gas oscillations in closed ducts are investigated by solving a previously derived, quasi-one-dimensional, nonlinear wave equation that accounts for forcing, gas dynamic nonlinearities, and viscous dissipation. This equation is solved with the approximate Galerkin method to determine the dependence of driven oscillations upon the duct shape, forcing frequency, and forcing amplitude. Initially, the applicability of the developed Galerkin solution approach was studied by investigating oscillations in a straight duct, closed at both ends and periodically oscillated at a single frequency. It is shown that the Galerkin method predictions of shock wave-like oscillations in such ducts are in excellent agreement with results obtained with other numerical solution techniques. Next, this study investigated the forced response of a class of horn-shaped ducts, and it is shown that for a given forcing amplitude, there exists a nonmonotonic increase in compression ratio as the duct's flare constant is increased. Finally, it is shown that oscillations driven in ducts whose shapes were chosen to provide shifting of the second and third natural acoustic mode frequencies exhibit significant waveform distortion and non-negligible increases in compression ratio when compared with oscillations driven in straight ducts.

Journal Article↗

PubMed2003

Domain walls in two-component dynamical lattices.

We introduce domain-wall (DW) states in the bimodal discrete nonlinear Schrödinger equation, in which the modes are coupled by cross-phase modulation (XPM). The results apply to an array of nonlinear optical waveguides carrying two different polarizations of light, or two different wavelengths, with anomalous intrinsic diffraction controlled by direction of the light beam, and to a string of drops of a binary Bose-Einstein condensate, trapped in an optical lattice. By means of continuation from various initial patterns taken in the anticontinuum (AC) limit, we find a number of different solutions of the DW type, for which different stability scenarios are identified. In the case of strong-XPM coupling, DW configurations contain a single mode at each end of the chain. The most fundamental solution of this type is found to be always stable. Another solution, which is generated by a different AC pattern, demonstrates behavior which is unusual for nonlinear dynamical lattices: it is unstable for small values of the coupling constant C (which measures the ratio of the nonlinearity and coupling lengths), and becomes stable at larger C. Stable bound states of DWs are also found. DW configurations generated by more sophisticated AC patterns are identified as well, but they are either completely unstable, or are stable only at small values of C. In the case of weak XPM, a natural DW solution is the one which contains a combination of both polarizations, with the phase difference between them 0 and pi at the opposite ends of the lattice. This solution is unstable at all values of C, but the instability is very weak for large C, indicating stabilization as the continuum limit is approached. The stability of DWs is also verified by direct simulations, and the evolution of unstable DWs is simulated too; in particular, it is found that, in the weak-XPM system, the instability may give rise to a moving DW. The DW states can be observed experimentally in the same parameter range where discrete solitons have been found in the lattice setting.

Journal Article↗

PubMed1999

Experimental observation of a torus-doubling transition to chaos near the ferroelectric phase transition of a KH2PO4 crystal.

A ferroelectric KH2PO4 crystal is implemented in a simple series connection of an RLC circuit and the transition to chaos near the phase-transition temperature is investigated. The torus-doubling scenario to chaos, the theory of which was expounded by Kaneko for high-dimensional dynamical systems, has been found in the crystal. These experimental results suggest that observation of the nonlinear dynamical behavior in condensed matter can give much information about the correlation between the generation of nonlinearity and the order-parameter dynamics of the crystal near the phase-transition temperature.

Journal Article↗

PubMed2001

Interpretation of analytical patterns from the output of chaotic dynamical memories.

A fundamental study has been carried out to use a nonlinear dynamic system, Freeman's KIII model, for pattern recognition in analytical chemistry. Filtering of the output of the neuron activity traces in the gamma range has been studied by applying a fast Fourier transform filter. Different possibilities for interpretation of the system output have been investigated. Preliminary results are demonstrated for classification of drugs based on their spectra in the mid infrared range.

Journal Article↗

PubMed2000

A signal-flow-graph approach to on-line gradient calculation.

A large class of nonlinear dynamic adaptive systems such as dynamic recurrent neural networks can be effectively represented by signal flow graphs (SFGs). By this method, complex systems are described as a general connection of many simple components, each of them implementing a simple one-input, one-output transformation, as in an electrical circuit. Even if graph representations are popular in the neural network community, they are often used for qualitative description rather than for rigorous representation and computational purposes. In this article, a method for both on-line and batch-backward gradient computation of a system output or cost function with respect to system parameters is derived by the SFG representation theory and its known properties. The system can be any causal, in general nonlinear and time-variant, dynamic system represented by an SFG, in particular any feedforward, time-delay, or recurrent neural network. In this work, we use discrete-time notation, but the same theory holds for the continuous-time case. The gradient is obtained in a straightforward way by the analysis of two SFGs, the original one and its adjoint (obtained from the first by simple transformations), without the complex chain rule expansions of derivatives usually employed. This method can be used for sensitivity analysis and for learning both off-line and on-line. On-line learning is particularly important since it is required by many real applications, such as digital signal processing, system identification and control, channel equalization, and predistortion.

Algorithms↗

PubMed2001

Symbolic dynamics and computation in model gene networks.

We analyze a class of ordinary differential equations representing a simplified model of a genetic network. In this network, the model genes control the production rates of other genes by a logical function. The dynamics in these equations are represented by a directed graph on an n-dimensional hypercube (n-cube) in which each edge is directed in a unique orientation. The vertices of the n-cube correspond to orthants of state space, and the edges correspond to boundaries between adjacent orthants. The dynamics in these equations can be represented symbolically. Starting from a point on the boundary between neighboring orthants, the equation is integrated until the boundary is crossed for a second time. Each different cycle, corresponding to a different sequence of orthants that are traversed during the integration of the equation always starting on a boundary and ending the first time that same boundary is reached, generates a different letter of the alphabet. A word consists of a sequence of letters corresponding to a possible sequence of orthants that arise from integration of the equation starting and ending on the same boundary. The union of the words defines the language. Letters and words correspond to analytically computable Poincare maps of the equation. This formalism allows us to define bifurcations of chaotic dynamics of the differential equation that correspond to changes in the associated language. Qualitative knowledge about the dynamics found by integrating the equation can be used to help solve the inverse problem of determining the underlying network generating the dynamics. This work places the study of dynamics in genetic networks in a context comprising both nonlinear dynamics and the theory of computation. (c) 2001 American Institute of Physics.

Journal Article↗

PubMed1999

Hyperchaotic qualities of the ball motion in a ball milling device.

Ball collisions in milling devices are governed by complex dynamics ruled by impredictable impulsive forces. In this paper, nonlinear dynamics techniques are employed to analyze the time series describing the trajectory of a milling ball in an empty container obtained from a numerical model. The attractor underlying the system dynamics was reconstructed by the time delay method. In order to characterize the system dynamics the calculation of the spectrum of Lyapunov exponents was performed. Six Lyapunov exponents, divided into two terns with opposite sign, were obtained. The detection of the positive tern demonstrates the occurrence of the hyperchaotic qualities of the ball motion. A fractal Lyapunov dimension, equal to 5.62, was also obtained confirming the strange features of the attractor. (c) 1999 American Institute of Physics.

Journal Article↗