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Results for “Nonlinear Dynamics”

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PubMed2002

Behavioral avoidance dynamics in the presence of a virtual spider.

Tracking behavior with a virtual spider and a neutral target is compared in fearful and nonfearful subjects. Head-tracking in virtual environments appears to be a scale-free behavior with long-range fractal-like patterns. Moreover, these fractal patterns change according to what the target affords the tracker and the level of behavioral avoidance manifested by the subjects. Results are interpreted in terms of ecological psychology and nonlinear dynamics, and implications for virtual reality (VR) psychology are outlined.

Adult↗

PubMed2005

Unusual Liénard-type nonlinear oscillator.

A Liénard type nonlinear oscillator of the form x+kxx+(k2/9)x3+lambda1x=0, which may also be considered as a generalized Emden-type equation, is shown to possess unusual nonlinear dynamical properties. It is shown to admit explicit nonisolated periodic orbits of conservative Hamiltonian type for lambda1>0. These periodic orbits exhibit the unexpected property that the frequency of oscillations is completely independent of amplitude and continues to remain as that of the linear harmonic oscillator. This is completely contrary to the standard characteristic property of nonlinear oscillators. Interestingly, the system though appears deceptively a dissipative type for lambda1< or =0 does admit a conserved Hamiltonian description, where the characteristic decay time is also independent of the amplitude. The results also show that the criterion for conservative Hamiltonian system in terms of divergence of flow function needs to be generalized.

Journal Article↗

PubMed2004

Long waves in streamwise varying shear flows: new mechanisms for a weakly nonlinear instability.

The weakly nonlinear dynamics of long waves embedded in marginally stable shear flows that vary in the streamwise direction are shown to be governed by a variable-coefficient Boussinesq equation. Depending on the local stability characteristics of the flow, new nonmodal or modal instabilities may emerge that serve as natural mechanisms for achieving amplitude thresholds necessary for weakly nonlinear instability and the transition to fully finite-amplitude states.

Journal Article↗

PubMed1999

Measurement of heart rate variability: a clinical tool or a research toy?

The objectives of this review are to discuss the diversity of mechanisms that may explain the association between heart rate (HR) variability and mortality, to appraise the clinical applicability of traditional and new measures of HR variability and to propose future directions in this field of research. There is a large body of data demonstrating that abnormal HR variability measured over a 24-h period provides information on the risk of subsequent death in subjects with and without structural heart disease. However, the mechanisms responsible for this association are not completely established. Therefore, no specific therapy is currently available to improve the prognosis for patients with abnormal HR variability. Reduced HR variability has been most commonly associated with a risk of arrhythmic death, but recent data suggest that abnormal variability also predicts vascular causes of death, progression of coronary atherosclerosis and death due to heart failure. A consensus is also lacking on the best HR variability measure for clinical purposes. Time and frequency domain measures of HR variability have been most commonly used, but recent studies show that new analysis methods based on nonlinear dynamics may be more powerful in terms of risk stratification. Before the measurement of HR variability can be applied to clinical practice and used to direct therapy, more precise insight into the pathophysiological link between HR variability and mortality are needed. Further studies should also address the issue of which of the HR variability indexes, including the new nonlinear measures, is best for clinical purposes in various patient populations.

Animals↗

PubMed2005

Multiscale brain modelling.

A central difficulty of brain modelling is to span the range of spatio-temporal scales from synapses to the whole brain. This paper overviews results from a recent model of the generation of brain electrical activity that incorporates both basic microscopic neurophysiology and large-scale brain anatomy to predict brain electrical activity at scales from a few tenths of a millimetre to the whole brain. This model incorporates synaptic and dendritic dynamics, nonlinearity of the firing response, axonal propagation and corticocortical and corticothalamic pathways. Its relatively few parameters measure quantities such as synaptic strengths, corticothalamic delays, synaptic and dendritic time constants, and axonal ranges, and are all constrained by independent physiological measurements. It reproduces quantitative forms of electroencephalograms seen in various states of arousal, evoked response potentials, coherence functions, seizure dynamics and other phenomena. Fitting model predictions to experimental data enables underlying physiological parameters to be inferred, giving a new non-invasive window into brain function that complements slower, but finer-resolution, techniques such as fMRI. Because the parameters measure physiological quantities relating to multiple scales, and probe deep structures such as the thalamus, this will permit the testing of a range of hypotheses about vigilance, cognition, drug action and brain function. In addition, referencing to a standardized database of subjects adds strength and specificity to characterizations obtained.

Axons↗

PubMed1992

Chaotic activity during iron-induced "epileptiform" discharge in rat hippocampal slices.

Low-dimensional chaotic dynamics have been suggested in the rat hippocampal slice during iron-induced epileptiform activity. The dimensionality of this chaotic activity has been found to be similar in slices bathed in the same ionic extracellular medium. Some slices also displayed a drop in dimensionality prior to the onset of seizure-like activity. We suggest that techniques of nonlinear dynamical analysis are a useful reverse-engineering tool for studying the in vitro brain slice. We further conclude that neuronal circuits capable of displaying chaotic activity could exist at the level of the in vitro brain slice.

Animals↗

PubMed1999

Analysis of cytokine dynamics in corneal allograft rejection.

Motivated by the discovery of oscillations in tumour necrosis factor-alpha (TNF-alpha) concentration in the aqueous humour of rabbits undergoing corneal allograft rejection, a simple mathematical model is developed for the regulation of TNF-alpha, which incorporates both negative feedback and amplification pathways. Mathematical analysis reveals a surprisingly rich behavioural repertoire for this simple cytokine pathway, including excitability, threshold behaviour, hysteresis, oscillations and bistability. This suggests new possibilities for experimental demonstration, and reveals the potential contributions of nonlinear dynamics to understanding cytokine regulation.

Animals↗

PubMed1995

Age-related changes in the "complexity" of cardiovascular dynamics: A potential marker of vulnerability to disease.

Healthy physiologic control of cardiovascular function is a result of complex interactions between multiple regulatory processes that operate over different time scales. These include the sympathetic and parasympathetic nervous systems which regulate beat-to-beat heart rate (HR) and blood pressure (BP), as well as extravascular volume, body temperature, and sleep which influence HR and BP over the longer term. Interactions between these control systems generate highly variable fluctuations in continuous HR and BP signals. Techniques derived from nonlinear dynamics and chaos theory are now being adapted to quantify the dynamic behavior of physiologic time series and study their changes with age or disease. We have shown significant age-related changes in the 1/f(x) relationship between the log amplitude and log frequency of the heart rate power spectrum, as well as declines in approximate dimension and approximate entropy of both heart rate and blood pressure time series. These changes in the "complexity" of cardiovascular dynamics reflect the breakdown and decoupling of integrated physiologic regulatory systems with aging, and may signal an impairment in cardiovascular ability to adapt to external and internal perturbations. Studies are currently underway to determine whether the complexity of HR or BP time series can distinguish patients with fainting spells due to benign vasovagal reactions from those due to life-threatening cardiac arrhythmias. Thus, measures of the complexity of physiologic variability may provide novel methods to monitor cardiovascular aging and test the efficacy of specific interventions to improve adaptive capacity in old age. (c) 1995 American Institute of Physics.

Journal Article↗

PubMed2025

Learning neural dynamics through instructive signals.

Rapid learning is essential for flexible behavior, but its basis in the brain remains unknown. Here we introduce the PRISM plasticity rule, a unifying mechanistic model of three well-established, fast-acting synaptic plasticity rules-in hippocampus, cerebellum and mushroom body-which relies exclusively on pre-synaptic activity and an "instructive signal" from another brain area. Using a multi-region network model we show that guiding PRISM plasticity with instructive signals enables the network to quickly learn extremely flexible nonlinear dynamics underlying behaviorally relevant computations, as well as to emulate unknown external system dynamics from real-time error signals, which we demonstrate with comprehensive simulations supported by exact mathematical theory. Thus, PRISM plasticity guided by instructive signals is well-suited to rapidly learn general-purpose neural computations-in contrast to canonical Hebbian rules. Finally, we show how including this plasticity rule in artificial learning algorithms can solve long-range temporal credit assignment, a long-standing challenge in machine learning.

cerebellum↗

PubMed1997

Three Centuries of Category Errors in Studies of the Neural Basis of Consciousness and Intentionality.

Recent interest in consciousness and the mind-brain problem has been fueled by technological advances in brain imaging and computer modeling in artificial intelligence: can machines be conscious? The machine metaphor originated in Cartesian "reflections" and culminated in 19th century reflexology modeled on Newtonian optics. It replaced the Aquinian view of mind, which was focused on the emergence of intentionality within the body, with control of output by input through brain dynamics. The state variables for neural activity were identified successively with animal spirits, élan vital, electricity, energy, information, and, most recently, Heisenbergian potentia. The source of dynamic structure in brains was conceived to lie outside brains in genetic and environmental determinism. An alternative view has grown in the 20th century from roots in American Pragmatists, particularly John Dewey, and European philosophers, particularly Heidegger and Piaget, by which brains are intrinsically unstable and continually create themselves. This view has new support from neurobiological studies in properties of self-organizing nonlinear dynamic systems. Intentional behavior can only be understood in relation to the chaotic patterns of neural activity that produce it. The machine metaphor remains, but the machine is seen as self-determining.

Journal Article↗

PubMed1999

Experimental studies of extinction dynamics

Extinction of populations occurs naturally, but global extinction rates are accelerating, making understanding extinction a high priority for conservation. Extinction in experimental populations of brine shrimp (Artemia franciscana) was measured to assess hypothesized extinction processes. Greater initial population size, greater maximum population size supported by the environment, and lower variation in environmental conditions reduced the likelihood of extinction, as hypothesized. However, initial population size was less important, and maximum population size and environmental variation were more important than often hypothesized. Unexpectedly, deterministic oscillations in population size due to inherent nonlinear dynamics and overcrowding were as important or more important than hypothesized processes.

Journal Article↗

PubMed2006

Dynamics of semiflexible polymers in a flow field.

We present a method to investigate the dynamics of a single semiflexible polymer, subject to anisotropic friction in a viscous fluid. In contrast to previous approaches, we do not rely on a discrete bead-rod model, but introduce a suitable normal mode decomposition of a continuous space curve. By means of a perturbation expansion for stiff filaments, we derive a closed set of coupled Langevin equations in mode space for the nonlinear dynamics in two dimensions, taking into account exactly the local constraint of inextensibility. The stochastic differential equations obtained this way are solved numerically, with parameters adjusted to describe the motion of actin filaments. As an example, we show results for the tumbling motion in shear flow.

Biopolymers↗

PubMed2001

Improvement of generalization ability for identifying dynamical systems by using universal learning networks.

This paper studies how the generalization ability of models of dynamical systems can be improved by taking advantage of the second order derivatives of the outputs with respect to the external inputs. The proposed method can be regarded as a direct implementation of the well-known regularization technique using the higher order derivatives of the Universal Learning Networks (ULNs). ULNs consist of a number of interconnected nodes where the nodes may have any continuously differentiable nonlinear functions in them and each pair of nodes can be connected by multiple branches with arbitrary time delays. A generalized learning algorithm has been derived for the ULNs, in which both the first order derivatives (gradients) and the higher order derivatives are incorporated. First, the method for computing the second order derivatives of ULNs is discussed. Then, a new method for implementing the regularization term is presented. Finally, simulation studies on identification of a nonlinear dynamical system with noises are carried out to demonstrate the effectiveness of the proposed method. Simulation results show that the proposed method can improve the generalization ability of neural networks significantly, especially in terms that (1) the robust network can be obtained even when the branches of trained ULNs are destructed, and (2) the obtained performance does not depend on the initial parameter values.

Computer Simulation↗

PubMed2001

Spatiotemporal variation of metabolism in a plant circadian rhythm: the biological clock as an assembly of coupled individual oscillators.

The complex dynamic properties of biological timing in organisms remain a central enigma in biology despite the increasingly precise genetic characterization of oscillating units and their components. Although attempts to obtain the time constants from oscillations of gene activity and biochemical units have led to substantial progress, we are still far from a full molecular understanding of endogenous rhythmicity and the physiological manifestations of biological clocks. Applications of nonlinear dynamics have revolutionized thinking in physics and in biomedical and life sciences research, and spatiotemporal considerations are now advancing our understanding of development and rhythmicity. Here we show that the well known circadian rhythm of a metabolic cycle in a higher plant, namely the crassulacean acid metabolism mode of photosynthesis, is expressed as dynamic patterns of independently initiated variations in photosynthetic efficiency (phi(PSII)) over a single leaf. Noninvasive highly sensitive chlorophyll fluorescence imaging reveals randomly initiated patches of varying phi(PSII) that are propagated within minutes to hours in wave fronts, forming dynamically expanding and contracting clusters and clearly dephased regions of phi(PSII). Thus, this biological clock is a spatiotemporal product of many weakly coupled individual oscillators, defined by the metabolic constraints of crassulacean acid metabolism. The oscillators operate independently in space and time as a consequence of the dynamics of metabolic pools and limitations of CO(2) diffusion between tightly packed cells.

Biological Clocks↗

PubMed2000

Theoretical considerations to the verification of dynamic multileaf collimated fields with a SLIC-type portal image detector.

The verification possibilities of dynamically collimated treatment beams with a scanning liquid ionization chamber electronic portal image device (SLIC-EPID) are investigated. The ion concentration in the liquid of a SLIC-EPID and therefore the read-out signal is determined by two parameters of a differential equation describing the creation and recombination of the ions. Due to the form of this equation, the portal image detector describes a nonlinear dynamic system with memory. In this work, the parameters of the differential equation were experimentally determined for the particular chamber in use and for an incident open 6 MV photon beam. The mathematical description of the ion concentration was then used to predict portal images of intensity-modulated photon beams produced by a dynamic delivery technique, the sliding window approach. Due to the nature of the differential equation, a mathematical condition for 'reliable leaf motion verification' in the sliding window technique can be formulated. It is shown that the time constants for both formation and decay of the equilibrium concentration in the chamber is in the order of seconds. In order to guarantee reliable leaf motion verification, these time constants impose a constraint on the rapidity of the image-read out for a given maximum leaf speed. For a leaf speed of 2 cm s(-1), a minimum image acquisition frequency of about 2 Hz is required. Current SLIC-EPID systems are usually too slow since they need about a second to acquire a portal image. However, if the condition is fulfilled, the memory property of the system can be used to reconstruct the leaf motion. It is shown that a simple edge detecting algorithm can be employed to determine the leaf positions. The method is also very robust against image noise.

Computer Simulation↗

PubMed1999

Sustained oscillations in living cells.

Glycolytic oscillations in yeast have been studied for many years simply by adding a glucose pulse to a suspension of cells and measuring the resulting transient oscillations of NADH. Here we show, using a suspension of yeast cells, that living cells can be kept in a well defined oscillating state indefinitely when starved cells, glucose and cyanide are pumped into a cuvette with outflow of surplus liquid. Our results show that the transitions between stationary and oscillatory behaviour are uniquely described mathematically by the Hopf bifurcation. This result characterizes the dynamical properties close to the transition point. Our perturbation experiments show that the cells remain strongly coupled very close to the transition. Therefore, the transition takes place in each of the cells and is not a desynchronization phenomenon. With these two observations, a study of the kinetic details of glycolysis, as it actually takes place in a living cell, is possible using experiments designed in the framework of nonlinear dynamics. Acetaldehyde is known to synchronize the oscillations. Our results show that glucose is another messenger substance, as long as the glucose transporter is not saturated.

Acetaldehyde↗

PubMed2004

Anisotropic diffraction and elliptic discrete solitons in two-dimensional waveguide arrays.

We demonstrate that both the linear (diffraction) and the nonlinear dynamics of two-dimensional waveguide arrays are considerably more complex and versatile than their one-dimensional counterparts. The discrete diffraction properties of these arrays can be effectively altered, depending on the propagation Bloch k-vector within the first Brillouin zone of the lattice. In general, this diffraction behavior is anisotropic and therefore permits the existence of a new class of discrete elliptic solitons in the nonlinear regime.

Journal Article↗

PubMed1996

Coordination of side-to-side head movements and walking in amphetamine-treated rats: a stereotyped motor pattern as a stable equilibrium in a dynamical system.

Rats injected with 5.0 mg/kg (+)-amphetamine perform, at one stage of the drug's influence, rhythmic side-to-side head movements while walking. This makes them an interesting preparation for investigating how stereotyped motor patterns emerge from the coordination of periodic movements. We report here such a pattern we have isolated: the left foreleg and the right hindleg land on the ground as the head reaches the peak of its movement to the right, and vice versa (contra-lateral pattern). We show that this pattern can be explained as a stable equilibrium in a simple, nonlinear dynamical model, similar to models developed for tapping with both hands in human subjects. The model also accounts for sequences of behavior that are not in the contra-lateral pattern, explaining them as a flow of the system back towards the stable equilibrium after a disturbance. Motor patterns that constitute the building blocks of unconstrained behavior are often defined as fixed phase relations between movements of the parts of the body. This study applies the paradigm of Dynamic Pattern Generation to free (unconstrained) behavior: motor patterns are defined as stable equilibria in dynamical systems, assembled by mutual influence of concurrent movements. Our findings suggest that this definition is more powerful for the description of free behavior. The amphetamine-treated rat is a useful preparation for investigating this notion in an unconstrained animal whose behavior is still not as complex and variable as that of the normal animal.

Amphetamine↗