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Results for “Nonlinear Dynamics”

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PubMed1992

Symmetry breaking dynamics of human multilimb coordination.

The dynamics of pattern formation and change are studied in a complex multicomponent system, specifically the arms and legs of human Ss. Among the novel features observed are differential stability of coordinative modes produced by limbs moving in the same versus different directions (Experiment 1); transitions between coordinative modes preceded by a slow drift in relative phase (Experiments 1 and 2); bifurcations or phase transitions from 1 four-limb pattern to another (Experiment 2); and spontaneous emergence of non-1:1-frequency- and phase-locked patterns, in addition to periods of relative coordination (Experiment 3). All observed relative phasing patterns and their dynamics (stability, loss of stability, intermittency) are shown to arise from the same underlying nonlinear dynamical structure, an important feature of which is broken symmetry.

Acceleration↗

PubMed2000

Dynamic algorithm for parameter estimation and its applications

We consider a dynamic method, based on synchronization and adaptive control, to estimate unknown parameters of a nonlinear dynamical system from a given scalar chaotic time series. We present an important extension of the method when the time series of a scalar function of the variables of the underlying dynamical system is given. We find that it is possible to obtain synchronization as well as parameter estimation using such a time series. We then consider a general quadratic flow in three dimensions and discuss the applicability of our method of parameter estimation in this case. In practical situations one expects only a finite time series of a system variable to be known. We show that the finite time series can be repeatedly used to estimate unknown parameters with an accuracy that improves and then saturates to a constant value with repeated use of the time series. Finally, we suggest an important application of the parameter estimation method. We propose that the method can be used to confirm the correctness of a trial function modeling an external unknown perturbation to a known system. We show that our method produces exact synchronization with the given time series only when the trial function has a form identical to that of the perturbation.

Journal Article↗

PubMed2004

Application of adaptive noise cancellation with neural-network-based fuzzy inference system for visual evoked potentials estimation.

This paper presents an application of adaptive noise cancellation with neural-network-based fuzzy inference system (NNFIS) for rapid estimation of visual evoked potentials (VEPs). Usually a recorded VEP is severely contaminated by background ongoing activities of the spontaneous EEG signal in the human brain. Many approaches have been adopted to enhance the signal-to-noise ratio (SNR) of the recorded signal. However, nonlinear dynamic methods are rarely investigated in view of their complexity, and the fact that the nonlinear characteristics of the signal are hard to determine in general. An adaptive noise cancellation method with NNFIS was carefully designed to estimate the VEP signal. NNFIS, based on Takagi and Sugeno's fuzzy model, has the advantage of being linear-in-parameter; thus the conventional adaptive methods can be efficiently utilized to estimate its parameters. Another advantage of NNFIS lies in that it can track the dynamic behavior of VEP in a real-time fashion because the VEP variation tracking is important for critical patient monitoring in the clinical situation. A series of computer experiments conducted on simulated and real-test responses have confirmed the superiority of the method developed in this paper.

Algorithms↗

PubMed1985

Nearly one dimensional dynamics in an epidemic.

The incidence of measles in New York City and Baltimore was studied using recently developed techniques in nonlinear dynamics. The data, monthly case reports for the years 1928-1963, suggest almost two dimensional, chaotic flows whose essential attributes are captured by one dimensional, unimodal maps. The effects of noise, inevitable in ecological and epidemiological systems are discussed.

Chickenpox↗

PubMed2005

Real-time nonlinear feedback control of pattern formation in (bio)chemical reaction-diffusion processes: a model study.

Theoretical and experimental studies related to manipulation of pattern formation in self-organizing reaction-diffusion processes by appropriate control stimuli become increasingly important both in chemical engineering and cellular biochemistry. In a model study, we demonstrate here exemplarily the application of an efficient nonlinear model predictive control (NMPC) algorithm to real-time optimal feedback control of pattern formation in a bacterial chemotaxis system modeled by nonlinear partial differential equations. The corresponding drift-diffusion model type is representative for many (bio)chemical systems involving nonlinear reaction dynamics and nonlinear diffusion. We show how the computed optimal feedback control strategy exploits the system inherent physical property of wave propagation to achieve desired control aims. We discuss various applications of our approach to optimal control of spatiotemporal dynamics.

Bacteria↗

PubMed2002

Transitions between dynamical states of differing stability in the human brain.

What mechanisms underlie the flexible formation, adaptation, synchronization, and dissolution of large-scale neural assemblies from the 10(10) densely interconnected, continuously active neurons of the human brain? Nonlinear dynamics provides a unifying perspective on self-organization. It shows that the emergence of patterns in open, nonequilibrium systems is governed by their stability in response to small disturbances and predicts macroscopic transitions between patterns of differing stability. Here, we directly demonstrate that such transitions can be elicited in the human brain by interference at the neural level. As a probe, we used a classic motor coordination paradigm exhibiting well described movement states of differing stability. Functional neuroimaging identified premotor (PMA) and supplementary motor (SMA) cortices as having neural activity linked to the degree of behavioral instability. These regions then were transiently disturbed with graded transcranial magnetic stimulation, which caused sustained and macroscopic behavioral transitions from the less stable out-of-phase to the stable in-phase movement, whereas the stable pattern could not be affected. Moreover, the strength of the disturbance needed (a measure of neural stability) was linked to the degree of behavioral stability, demonstrating the applicability of nonlinear system theory as a powerful predictor of the dynamical repertoire of the human brain.

Adult↗

PubMed2003

Transients and attractors in epidemics.

Historical records of childhood disease incidence reveal complex dynamics. For measles, a simple model has indicated that epidemic patterns represent attractors of a nonlinear dynamic system and that transitions between different attractors are driven by slow changes in birth rates and vaccination levels. The same analysis can explain the main features of chickenpox dynamics, but fails for rubella and whooping cough. We show that an additional (perturbative) analysis of the model, together with knowledge of the population size in question, can account for all the observed incidence patterns by predicting how stochastically sustained transient dynamics should be manifested in these systems.

Child↗

PubMed2001

Optical pulse propagation in nonlinear photonic crystals.

We present a formalism for optical pulse propagation in nonlinear photonic crystals of arbitrary dimensionality. Using a multiple-scale analysis, we derive the dynamical nonlinear Schrödinger equation obeyed by the envelope function modulating an underlying Bloch function. Effective coefficients appear in that equation characterizing the effects of Kerr nonlinearity, linear gain or loss, and material dispersion. They depend on how the underlying Bloch function "samples" these effects in the photonic crystal, and require for their calculation a specification of these effects throughout the photonic crystal, and the calculated bandstructure of the photonic crystals in the linear, nondispersive limit. We show that wave packets from different bands can experience significantly modified effective material properties.

Journal Article↗

PubMed1996

Discrimination of sleep stages: a comparison between spectral and nonlinear EEG measures.

During recent years, methods from nonlinear dynamics were introduced into the analysis of EEG signals. Although from a theoretical point of view nonlinear measures quantify properties being independent from conventional spectral measures, it is a crucial question whether in practice nonlinear EEG measures yield additional information, which is not redundant to the information gained by spectral analysis. Therefore, we compared the ability of several spectral and nonlinear measures to discriminate different sleep stages. We evaluated spectral measures (relative delta power, spectral edge, spectral entropy and first spectral moment), and nonlinear measures (correlation dimension D2, largest Lyapunov exponent LI, and approximated Kolmogorof entropy K2), and additionally the stochastic time domain based measure entropy of amplitudes. For 12 healthy subjects these measures were calculated from sleep EEG segments of 2:44 min duration, each segment unambiguously corresponding to one of the sleep stages I, II, SWS and REM. Results were statistically evaluated by multivariate and univariate analyses of variance and by discriminant analyses. Generally, nonlinear measures (D2 and L1) performed better in discriminating sleep stages I and II, whereas spectral measures showed advantages in discriminating stage II and SWS. Combinations of spectral and nonlinear measures yielded a better overall discrimination of sleep stages than spectral measures alone. The best overall discrimination was reached even without inclusion of any of the spectral measures. It can be concluded that nonlinear measures yield additional information, which improves the ability to discriminate sleep stages and which may in general improve the ability to distinguish different psychophysiological states. This confirms the importance and practical reliability of the application of nonlinear methods to EEG analysis.

Adult↗

PubMed1994

Presenting joint kinematics of human locomotion using phase plane portraits and Poincaré maps.

Additional graphical tools are needed to better visualize the joint kinematics of human locomotion. Standard plots in which the joint displacements are plotted against time or percent gait cycle do not provide sufficient information about the dynamics of the system. In this article, a study based on the two graphical tools of nonlinear dynamics to visualize the steady-state kinematics of human gait is presented. An experimental setup was developed to acquire the necessary data for application of the techniques. Twenty young adults, whose medical histories are free of gait pathology, were tested. Computerized electrogoniometers and foot switches were used to measure the kinematic data of the lower extremities and capture four instants of the gait cycle: heel strike, foot flat, heel off, and toe off. Phase plane portraits of each joint were constructed for the sagittal plane by plotting angular velocity against angular displacement. Poincaré maps were obtained by periodically sampling the joint profiles at toe off and plotting the ith iterate against the (i + 1)th one. Phase plane portraits are useful in monitoring the variations of joint velocity and position on the same graph in a more compact form. Poincaré maps are effective in differentiating steady gait from transient locomotion.

Adult↗

PubMedDate not supplied

Analysis of electrically induced reentrant circuits in a sheet of myocardium.

Understanding the complex spatiotemporal dynamics of action potential propagation in the heart during arrhythmia is exceedingly difficult. This study applies nonlinear dynamics tools to simplify this task. Using the results of a simulation of an electrical induction of reentry in a sheet of myocardium represented as a bidomain, transmembrane voltage maps are processed to obtain: (i) spatial maps of phase angle and phase singularity trajectories, (ii) state scatter plots, and (iii) spatial maps of even phase resetting, wave fronts and wave tails. Tracking the phase singularities allows us to identify the "seeds" of reentry before the reentrant circuit is formed and to characterize the spatiotemporal evolution of the organizing center of the reentrant circuit. The state scatter plots demonstrate the effect of the shock on the instantaneous state of the system. The spatial maps of even phase resetting allow us to identify the shock-induced excitable gaps (regions of regenerative repolarization) as well as the regions directly activated by the shock. These nontraditional approaches to the analysis of electrophysiological phenomena greatly enhance our ability to conceptualize the dynamics of arrhythmias.

Action Potentials↗

PubMed2005

Positive affect and the complex dynamics of human flourishing.

Extending B. L. Fredrickson's (1998) broaden-and-build theory of positive emotions and M. Losada's (1999) nonlinear dynamics model of team performance, the authors predict that a ratio of positive to negative affect at or above 2.9 will characterize individuals in flourishing mental health. Participants (N=188) completed an initial survey to identify flourishing mental health and then provided daily reports of experienced positive and negative emotions over 28 days. Results showed that the mean ratio of positive to negative affect was above 2.9 for individuals classified as flourishing and below that threshold for those not flourishing. Together with other evidence, these findings suggest that a set of general mathematical principles may describe the relations between positive affect and human flourishing.

Adult↗

PubMed2004

Optically induced dynamics in nematic liquid crystals: The role of finite beam size.

We report on the influence of a finite beam size on the molecular reorientation dynamics when a nematic liquid crystal film is excited by a laser beam. We present experimental evidence of a new class of nonlinear dynamics when the excitation is a Gaussian shaped, circularly polarized laser beam at normal incidence. Various nonlinear regimes, periodic, quasiperiodic, intermittent, and possibly chaotic, are observed. A physical interpretation based on walk-off effects is proposed and its implications on current research in the field are discussed.

Journal Article↗

PubMed2004

Rich example of geometrically induced nonlinearity: from rotobreathers and kinks to moving localized modes and resonant energy transfer.

We present an experimentally realizable, simple mechanical system with linear interactions whose geometric nature leads to nontrivial, nonlinear dynamical equations. The equations of motion are derived and their ground state structures are analyzed. Selective "static" features of the model are examined in the context of nonlinear waves including rotobreathers and kinklike solitary waves. We also explore "dynamic" features of the model concerning the resonant transfer of energy and the role of moving intrinsic localized modes in the process.

Journal Article↗

PubMed2004

Tolerance mechanisms and recent progress.

There has been tremendous progress in our understanding of the mechanisms mediating allograft tolerance, which have been revealed to be far more complex and regulated than hitherto suspected. New results have enriched our understanding of the relative contributions of the direct and indirect pathways to immunity and tolerance over time. The role of central tolerance has been expanded with the surprising discovery of "ectopic" or "promiscuous" antigens expressed by medullary thymic epithelial cells, and the function of the thymus in generating naturally occurring CD4+ CD25+ regulatory T cells. In the periphery, it is increasingly appreciated that tolerance is a highly active process, with tolerogenic dendritic cells and regulatory T cells being the major players. However, the challenge of understanding the complex interactions regulating the dynamic balance between immunity and tolerance are formidable, and new tools from the more formal disciplines of nonlinear dynamics and systems engineering may help provide insight. Although many hurdles remain, the progress in elucidating the basic mechanisms of tolerance is rapidly being translated into clinical trials and provides grounds for optimism that clinical tolerance will eventually become a reality.

Dendritic Cells↗

PubMed2006

Scaling behavior in mitochondrial redox fluctuations.

Scale-invariant long-range correlations have been reported in fluctuations of time-series signals originating from diverse processes such as heart beat dynamics, earthquakes, and stock market data. The common denominator of these apparently different processes is a highly nonlinear dynamics with competing forces and distinct feedback species. We report for the first time an experimental evidence for scaling behavior in NAD(P)H signal fluctuations in isolated mitochondria and intact cells isolated from the liver of a young (5-month-old) mouse. Time-series data were collected by two-photon imaging of mitochondrial NAD(P)H fluorescence and signal fluctuations were quantitatively analyzed for statistical correlations by detrended fluctuation analysis and spectral power analysis. Redox [NAD(P)H / NAD(P)(+)] fluctuations in isolated mitochondria and intact liver cells were found to display nonrandom, long-range correlations. These correlations are interpreted as arising due to the regulatory dynamics operative in Krebs' cycle enzyme network and electron transport chain in the mitochondria. This finding may provide a novel basis for understanding similar regulatory networks that govern the nonequilibrium properties of living cells.

Animals↗

PubMed2000

Twirling and whirling: viscous dynamics of rotating elastic filaments.

Motivated by diverse phenomena in cellular biophysics, including bacterial flagellar motion and DNA transcription and replication, we study the overdamped nonlinear dynamics of a rotationally forced filament with twist and bend elasticity. Competition between twist injection, twist diffusion, and writhing instabilities is described by coupled PDEs for twist and bend evolution. Analytical and numerical methods elucidate the twist/bend coupling and reveal two regimes separated by a Hopf bifurcation: (i) diffusion-dominated axial rotation, or twirling, and (ii) steady-state crankshafting motion, or whirling. The consequences of these phenomena for self-propulsion are investigated, and experimental tests proposed.

Bacterial Physiological Phenomena↗

PubMed2002

Possible neural coding with interevent intervals of synchronous firing.

Neural networks composed of excitable neurons with noise generate rich nonlinear dynamics with spatiotemporal structures of neuronal spikes. Among various spatiotemporal patterns of spikes, synchronous firing has been studied most extensively both with physiological experimentation and with theoretical analysis. In this paper, we consider nonlinear neurodynamics in terms of synchronous firing and possibility of neural coding with such synchronous firing, which may be used in the "noisy brain." In particular, reconstruction of a chaotic attractor modeling a dynamical environment is explored with interevent intervals of synchronous firing from the perspective of nonlinear time series analysis and stochastic resonance.

Journal Article↗