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All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Nonlinear dynamics, chaos and complex cardiac arrhythmias

Periodic stimulation of a nonlinear cardiac oscillator in vitro gives rise to complex dynamics that is well described by one-dimensional finite difference equations. As stimulation parameters are varied, a large number of different phase-locked and chaotic rhythms is observed. Similar rhythms can be observed in the intact human heart when there is interaction between two pacemaker sites. Simplified models are analyzed, which show some correspondence to clinical observations.

Glass, L.↗
NASA NTRS1991

The Applicability of Nonlinear Systems Dynamics Chaos Measures to Cardiovascular Physiology Variables

Three measures of nonlinear chaos (fractal dimension, Approximate Entropy (ApEn), and Lyapunov exponents) were studied as potential measures of cardiovascular condition. It is suggested that these measures have potential in the assessment of cardiovascular condition in environments of normal cardiovascular stress (normal gravity on the Earth surface), cardiovascular deconditioning (microgravity of space), and increased cardiovascular stress (lower body negative pressure (LBNP) treatments).

Hooker, John C.↗
NASA NTRS1987

An algebraic criterion for the onset of chaos in nonlinear dynamic systems

The correspondence between iterated integrals and a noncommutative algebra is used to recast the given dynamical system from the time domain to the Laplace-Borel transform domain. It is then shown that the following algebraic criterion has to be satisfied for the outset of chaos: the limit (as tau approaches infinity and x sub 0 approaches infinity) of ((sigma(k=0) (tau sup k) / (k* x sub 0 sup k)) G II G = 0, where G is the generating power series of the trajectories, the symbol II is the shuffle product (le melange) of the noncommutative algebra, x sub 0 is a noncommutative variable, and tau is the correlation parameter. In the given equation, symbolic forms for both G and II can be obtained by use of one of the currently available symbolic languages such as PLI, REDUCE, and MACSYMA. Hence, the criterion is a computer-algebraic one.

Unal, A.↗
NASA NTRS1986

Chaos and nonlinear dynamics of single-particle orbits in a magnetotaillike magnetic field

The properties of charged-particle motion in Hamiltonian dynamics are studied in a magnetotaillike magnetic field configuration. It is shown by numerical integration of the equation of motion that the system is generally nonintegrable and that the particle motion can be classified into three distinct types of orbits: bounded integrable orbits, unbounded stochastic orbits, and unbounded transient orbits. It is also shown that different regions of the phase space exhibit qualitatively different responses to external influences. The concept of 'differential memory' in single-particle distributions is proposed. Physical implications for the dynamical properties of the magnetotail plasmas and the possible generation of non-Maxwellian features in the distribution functions are discussed.

Chen, J.↗
NASA NTRS1999

Cardiac interbeat interval dynamics from childhood to senescence : comparison of conventional and new measures based on fractals and chaos theory

BACKGROUND: New methods of R-R interval variability based on fractal scaling and nonlinear dynamics ("chaos theory") may give new insights into heart rate dynamics. The aims of this study were to (1) systematically characterize and quantify the effects of aging from early childhood to advanced age on 24-hour heart rate dynamics in healthy subjects; (2) compare age-related changes in conventional time- and frequency-domain measures with changes in newly derived measures based on fractal scaling and complexity (chaos) theory; and (3) further test the hypothesis that there is loss of complexity and altered fractal scaling of heart rate dynamics with advanced age. METHODS AND RESULTS: The relationship between age and cardiac interbeat (R-R) interval dynamics from childhood to senescence was studied in 114 healthy subjects (age range, 1 to 82 years) by measurement of the slope, beta, of the power-law regression line (log power-log frequency) of R-R interval variability (10(-4) to 10(-2) Hz), approximate entropy (ApEn), short-term (alpha(1)) and intermediate-term (alpha(2)) fractal scaling exponents obtained by detrended fluctuation analysis, and traditional time- and frequency-domain measures from 24-hour ECG recordings. Compared with young adults (<40 years old, n=29), children (<15 years old, n=27) showed similar complexity (ApEn) and fractal correlation properties (alpha(1), alpha(2), beta) of R-R interval dynamics despite lower spectral and time-domain measures. Progressive loss of complexity (decreased ApEn, r=-0.69, P<0.001) and alterations of long-term fractal-like heart rate behavior (increased alpha(2), r=0.63, decreased beta, r=-0.60, P<0.001 for both) were observed thereafter from middle age (40 to 60 years, n=29) to old age (>60 years, n=29). CONCLUSIONS: Cardiac interbeat interval dynamics change markedly from childhood to old age in healthy subjects. Children show complexity and fractal correlation properties of R-R interval time series comparable to those of young adults, despite lower overall heart rate variability. Healthy aging is associated with R-R interval dynamics showing higher regularity and altered fractal scaling consistent with a loss of complex variability.

NASA Discipline Cardiopulmonary↗
NASA NTRS1994

Effects of head-down bed rest on complex heart rate variability: Response to LBNP testing

Head-down bed rest is used to model physiological changes during spaceflight. We postulated that bed rest would decrease the degree of complex physiological heart rate variability. We analyzed continuous heart rate data from digitized Holter recordings in eight healthy female volunteers (age 28-34 yr) who underwent a 13-day 6 deg head-down bed rest study with serial lower body negative pressure (LBNP) trials. Heart rate variability was measured on a 4-min data sets using conventional time and frequency domain measures as well as with a new measure of signal 'complexity' (approximate entropy). Data were obtained pre-bed rest (control), during bed rest (day 4 and day 9 or 11), and 2 days post-bed rest (recovery). Tolerance to LBNP was significantly reduced on both bed rest days vs. pre-bed rest. Heart rate variability was assessed at peak LBNP. Heart rate approximate entropy was significantly decreased at day 4 and day 9 or 11, returning toward normal during recovery. Heart rate standard deviation and the ratio of high- to low-power frequency did not change significantly. We conclude that short-term bed rest is associated with a decrease in the complex variability of heart rate during LBNP testing in healthy young adult women. Measurement of heart rate complexity, using a method derived from nonlinear dynamics ('chaos theory'), may provide a sensitive marker of this loss of physiological variability, complementing conventional time and frequency domain statistical measures.

Goldberger, Ary L.↗
NASA NTRS1994

Gender- and age-related differences in heart rate dynamics: are women more complex than men?

OBJECTIVES. This study aimed to quantify the complex dynamics of beat-to-beat sinus rhythm heart rate fluctuations and to determine their differences as a function of gender and age. BACKGROUND. Recently, measures of heart rate variability and the nonlinear "complexity" of heart rate dynamics have been used as indicators of cardiovascular health. Because women have lower cardiovascular risk and greater longevity than men, we postulated that there are important gender-related differences in beat-to-beat heart rate dynamics. METHODS. We analyzed heart rate dynamics during 8-min segments of continuous electrocardiographic recording in healthy young (20 to 39 years old), middle-aged (40 to 64 years old) and elderly (65 to 90 years old) men (n = 40) and women (n = 27) while they performed spontaneous and metronomic (15 breaths/min) breathing. Relatively high (0.15 to 0.40 Hz) and low (0.01 to 0.15 Hz) frequency components of heart rate variability were computed using spectral analysis. The overall "complexity" of each heart rate time series was quantified by its approximate entropy, a measure of regularity derived from nonlinear dynamics ("chaos" theory). RESULTS. Mean heart rate did not differ between the age groups or genders. High frequency heart rate power and the high/low frequency power ratio decreased with age in both men and women (p < 0.05). The high/low frequency power ratio during spontaneous and metronomic breathing was greater in women than men (p < 0.05). Heart rate approximate entropy decreased with age and was higher in women than men (p < 0.05). CONCLUSIONS. High frequency heart rate spectral power (associated with parasympathetic activity) and the overall complexity of heart rate dynamics are higher in women than men. These complementary findings indicate the need to account for gender-as well as age-related differences in heart rate dynamics. Whether these gender differences are related to lower cardiovascular disease risk and greater longevity in women requires further study.

NASA Discipline Cardiopulmonary↗
NASA NTRS1991

Aging and the complexity of cardiovascular dynamics

Biomedical signals often vary in a complex and irregular manner. Analysis of variability in such signals generally does not address directly their complexity, and so may miss potentially useful information. We analyze the complexity of heart rate and beat-to-beat blood pressure using two methods motivated by nonlinear dynamics (chaos theory). A comparison of a group of healthy elderly subjects with healthy young adults indicates that the complexity of cardiovascular dynamics is reduced with aging. This suggests that complexity of variability may be a useful physiological marker.

Non-NASA Center↗
NASA NTRS1996

Turbulent Fluid Motion 6: Turbulence, Nonlinear Dynamics, and Deterministic Chaos

Several turbulent and nonturbulent solutions of the Navier-Stokes equations are obtained. The unaveraged equations are used numerically in conjunction with tools and concepts from nonlinear dynamics, including time series, phase portraits, Poincare sections, Liapunov exponents, power spectra, and strange attractors. Initially neighboring solutions for a low-Reynolds-number fully developed turbulence are compared. The turbulence is sustained by a nonrandom time-independent external force. The solutions, on the average, separate exponentially with time, having a positive Liapunov exponent. Thus, the turbulence is characterized as chaotic. In a search for solutions which contrast with the turbulent ones, the Reynolds number (or strength of the forcing) is reduced. Several qualitatively different flows are noted. These are, respectively, fully chaotic, complex periodic, weakly chaotic, simple periodic, and fixed-point. Of these, we classify only the fully chaotic flows as turbulent. Those flows have both a positive Liapunov exponent and Poincare sections without pattern. By contrast, the weakly chaotic flows, although having positive Liapunov exponents, have some pattern in their Poincare sections. The fixed-point and periodic flows are nonturbulent, since turbulence, as generally understood, is both time-dependent and aperiodic.

Deissler, Robert G.↗
NASA NTRS1994

EEG and chaos: Description of underlying dynamics and its relation to dissociative states

The goal of this work is the identification of states especially as related to the process of error production and lapses of awareness as might be experienced during aviation. Given the need for further articulation of the characteristics of 'error prone state' or 'hazardous state of awareness,' this NASA grant focused on basic ground work for the study of the psychophysiology of these states. In specific, the purpose of this grant was to establish the necessary methodology for addressing three broad questions. The first is how the error prone state should be conceptualized, and whether it is similar to a dissociative state, a hypnotic state, or absent mindedness. Over 1200 subjects completed a variety of psychometric measures reflecting internal states and proneness to mental lapses and absent mindedness; the study suggests that there exists a consistency of patterns displayed by individuals who self-report dissociative experiences such that those individuals who score high on measures of dissociation also score high on measures of absent mindedness, errors, and absorption, but not on scales of hypnotizability. The second broad question is whether some individuals are more prone to enter these states than others. A study of 14 young adults who scored either high or low on the dissociation experiences scale performed a series of six tasks. This study suggests that high and low dissociative individuals arrive at the experiment in similar electrocortical states and perform cognitive tasks (e.g., mental math) in a similar manner; it is in the processing of internal emotional states that differences begin to emerge. The third question to be answered is whether recent research in nonlinear dynamics, i.e., chaos, offer an addition and/or alternative to traditional signal processing methods, i.e., fast Fourier transforms, and whether chaos procedures can be modified to offer additional information useful in identifying brain states. A preliminary review suggests that current nonlinear dynamical techniques such as dimensional analysis can be successfully applied to electrocortical activity. Using the data set developed in the study of the young adults, chaos analyses using the Farmer algorithm were performed; it is concluded that dimensionality measures reflect information not contained in traditional EEG Fourier analysis.

Ray, William J.↗
NASA NTRS2002

Dynamical Approach Study of Spurious Numerics in Nonlinear Computations

The last two decades have been an era when computation is ahead of analysis and when very large scale practical computations are increasingly used in poorly understood multiscale complex nonlinear physical problems and non-traditional fields. Ensuring a higher level of confidence in the predictability and reliability (PAR) of these numerical simulations could play a major role in furthering the design, understanding, affordability and safety of our next generation air and space transportation systems, and systems for planetary and atmospheric sciences, and in understanding the evolution and origin of life. The need to guarantee PAR becomes acute when computations offer the ONLY way of solving these types of data limited problems. Employing theory from nonlinear dynamical systems, some building blocks to ensure a higher level of confidence in PAR of numerical simulations have been revealed by the author and world expert collaborators in relevant fields. Five building blocks with supporting numerical examples were discussed. The next step is to utilize knowledge gained by including nonlinear dynamics, bifurcation and chaos theories as an integral part of the numerical process. The third step is to design integrated criteria for reliable and accurate algorithms that cater to the different multiscale nonlinear physics. This includes but is not limited to the construction of appropriate adaptive spatial and temporal discretizations that are suitable for the underlying governing equations. In addition, a multiresolution wavelets approach for adaptive numerical dissipation/filter controls for high speed turbulence, acoustics and combustion simulations will be sought. These steps are corner stones for guarding against spurious numerical solutions that are solutions of the discretized counterparts but are not solutions of the underlying governing equations.

Yee, H. C.↗
NASA NTRS1986

Physics through the 1990s: Condensed-matter physics

The volume presents the current status of condensed-matter physics from developments since the 1970s to opportunities in the 1990s. Topics include electronic structure, vibrational properties, critical phenomena and phase transitions, magnetism, semiconductors, defects and diffusion, surfaces and interfaces, low-temperature physics, liquid-state physics, polymers, nonlinear dynamics, instabilities, and chaos. Appendices cover the connections between condensed-matter physics and applications of national interest, new experimental techniques and materials, laser spectroscopy, and national facilities for condensed-matter physics research. The needs of the research community regarding support for individual researchers and for national facilities are presented, as are recommendations for improved government-academic-industrial relations.

Source record↗
NASA NTRS1999

Chaos in Magnetoplasmas

A nonlinear wave, in general, is equivalent to a nonlinear dynamical system, which exhibits the phenomena of chaos.

chaos magnetoplasmas nonlinear↗
NASA NTRS1991

An unpredictable-dynamics approach to neural intelligence

The theoretical basis for a dynamic neural network architecture that takes advantage of the notion of terminal chaos to process information in a way that is phenomenologically similar to brain activity is presented. The architecture exploits the phenomenology of nonlinear dynamic systems as an alternative to the traditional paradigm of finite-state machines. It is based on some effects of non-Lipschitzian dynamics. The nonlinear phenomenon of terminal chaos and its relevance to brain activity are examined.

Zak, Michail↗
NASA NTRS1997

Chaotic Time Series Analysis Method Developed for Stall Precursor Identification in High-Speed Compressors

A new technique for rotating stall precursor identification in high-speed compressors has been developed at the NASA Lewis Research Center. This pseudo correlation integral method uses a mathematical algorithm based on chaos theory to identify nonlinear dynamic changes in the compressor. Through a study of four various configurations of a high-speed compressor stage, a multistage compressor rig, and an axi-centrifugal engine test, this algorithm, using only a single pressure sensor, has consistently predicted the onset of rotating stall.

Source record↗
NASA NTRS1992

Nonlinear vibration and radiation from a panel with transition to chaos

The dynamic response of an aircraft panel forced at resonance and off-resonance by plane acoustic waves at normal incidence is investigated experimentally and numerically. Linear, nonlinear (period doubling), and chaotic responses are obtained by increasing the sound pressure level of the excitation. The response time history is sensitive to the input level and to the frequency of excitation. The change in response behavior is due to a change in input conditions, triggered either naturally or by modulation of the bandwidth of the incident waves. Off-resonance bifurcation is diffused and difficult to maintain; thus the panel response drifts into a linear behavior. The acoustic pressure emanated by the panel is either linear or nonlinear as is the vibration response. The nonlinear effects accumulate during the propagation with distance. Results are also obtained on the control of the panel response using damping tape on an aluminum panel and a graphite epoxy panel having the same size and weight. Good agreement is obtained betwen the experimental and numerical results.

Maestrello, Lucio↗
NASA NTRS1990

An introduction to chaos theory in CFD

The popular subject 'chaos theory' has captured the imagination of a wide variety of scientists and engineers. CFD has always been faced with nonlinear systems and it is natural to assume that nonlinear dynamics will play a role at sometime in such work. This paper will attempt to introduce some of the concepts and analysis procedures associated with nonlinear dynamics theory. In particular, results from computations of an airfoil at high angle of attack which exhibits a sequence of bifurcations for single frequency unsteady shedding through period doublings cascading into low dimensional chaos are used to present and demonstrate various aspects of nonlinear dynamics in CFD.

Pulliam, Thomas H.↗
NASA NTRS1987

Deterministic representation of chaos with application to turbulence

Chaotic motions of nonlinear dynamical systems are decomposed into mean components and fluctuations. The approach is based upon the concept that the fluctuations driven by the instability of the original (unperturbed) motion grow until a new stable state is approached. The Reynolds-type equations written for continuous as well as for finite-degrees-of-freedom dynamical systems are closed by using this stabilization principle. The theory is applied to conservative systems, to strange attractors and to turbulent motions.

Zak, M.↗