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PubMed2006

Representation of dynamic events triggered by motion lines and static human postures.

Artists and cartoonists are able to dexterously depict a running person on paper with the aid of 'motion lines'. We scientifically examined whether the cognitive system can exploit motion lines in constructing memory representations of the location of a running person depicted in a still image. A target depicting a standing or a running person with or without motion lines was presented to participants for 500 ms. Observers were required to reproduce the location of the target 1 s after its disappearance. Data from depicted leftward and rightward moving persons were collapsed. Memory displacement of the target was shown to be largest in the presence of motion lines and a posture indicating an identical direction of movement. By assessing the absolute localization error, we showed that there was no localization advantage toward a target with a symmetrical (standing) posture over one with an asymmetrical (running) posture. Our findings indicate synergetic interaction between the mechanisms responsible for processing of motion lines and human postures in the representation of dynamic events.

Analysis of Variance↗
PubMed2002

Detecting determinism in short time series, with an application to the analysis of a stationary EEG recording.

We have developed a new method for detecting determinism in a short time series and used this method to examine whether a stationary EEG is deterministic or stochastic. The method is based on the observation that the trajectory of a time series generated from a differentiable dynamical system behaves smoothly in an embedded phase space. The angles between two successive directional vectors in the trajectory reconstructed from a time series at a minimum embedding dimension were calculated as a function of time. We measured the irregularity of the angle variations obtained from the time series using second-order difference plots and central tendency measures, and compared these values with those from surrogate data. The ability of the proposed method to distinguish between chaotic and stochastic dynamics is demonstrated through a number of simulated time series, including data from Lorenz, Rössler, and Van der Pol attractors, high-dimensional equations, and 1/f noise. We then applied this method to the analysis of stationary segments of EEG recordings consisting of 750 data points (6-s segments) from five normal subjects. The stationary EEG segments were not found to exhibit deterministic components. This method can be used to analyze determinism in short time series, such as those from physiological recordings, that can be modeled using differentiable dynamical processes.

Algorithms↗
PubMedDate not supplied

Chaos control and synchronization, with input saturation, via recurrent neural networks.

This paper deals with the adaptive tracking problem of non-linear systems in presence of unknown parameters, unmodelled dynamics and input saturation. A high order recurrent neural network is used in order to identify the unknown system and a learning law is obtained using the Lyapunov methodology. Then a stabilizing control law for the reference tracking error dynamics is developed using the Lyapunov methodology and the Sontag control law. Tracking error boundedness is established as a function of a design parameter. The new approach is illustrated by examples of complex dynamical systems: chaos control and synchronization.

Neural Networks, Computer↗
PubMed2000

Advantages of rhythmic movements at resonance: minimal active degrees of freedom, minimal noise, and maximal predictability.

Using time delay embedding, the authors applied phase space reconstruction to the time series of rhythmic movements of a hand-held pendulum. Subjects (N = 6) produced the manual oscillations about the wrist at the pendulum's resonant frequency and at a higher and a lower frequency. The number of active degrees of freedom required to capture the dynamics of the rhythmic behavior was 3 for the resonant frequency and 4 for each of the nonresonant frequencies. The residual high-dimensional noise was similarly lowest for the resonant frequency. Whereas 33% and 20%, respectively, of the vectors in the phase spaces of the dynamics higher and lower than resonance were unpredictable, only 12% were unpredictable at resonance. Finally, the predictability of the evolving dynamics extended farther into the future for oscillations at the resonant frequency. At resonance, the prediction horizon was 5 times farther than the prediction horizon for the higher than resonance behavior and 2.5 times farther than that for the lower than resonance behavior. The results suggest that, in pendular oscillations of a limb or limb segment, attunement of the central nervous system to the resonant frequency minimizes the variables to be controlled and maximizes the predictability of the rhythmic movement's chaotic dynamics.

Forecasting↗
PubMed2006

The scale transition: scaling up population dynamics with field data.

Applying the recent developments of scale transition theory, we demonstrate a systematic approach to the problem of scaling up local scale interactions to regional scale dynamics with field data. Dynamics on larger spatial scales differ from the predictions of local dynamics alone because of an interaction between nonlinearity in population dynamics at the local scale and spatial variation in density and environmental factors over the regional population. Our systematic approach to scaling up involves the following five steps. First, define a model for dynamics on the local spatial scale. Second, apply scale transition theory to identify key interactions between nonlinearity and spatial variation that translate local dynamics to the regional scale. Third, measure local-scale model parameters to determine nonlinearities at local scales. Fourth, measure spatial variation. Finally, combine nonlinearity and variation measures to obtain the scale transition. Using field data for the dynamics of grazers and periphyton in a freshwater stream, we show that scale transition terms greatly reduce the growth and equilibrium density of the periphyton population at the stream scale compared to rock scale populations, confirming the importance of spatial mechanisms to stream-scale dynamics.

Ecosystem↗
PubMed1994

Dynamic modeling, chaos, and cognitive development.

We provide an introduction to the essential constructs involved in dynamic modeling. These constructs are then related to issues in psychological development. In particular, we discuss stages, states, sequences, and pure transition models as well as cross-sectional and longitudinal experimental designs. We conclude that transition is a key invariance in development and that single subject, longitudinal designs are essential in studying the dynamics of ontogeny.

Child↗
PubMed1999

The effect of slow allosteric transitions in a coupled biochemical oscillator model.

The effect of slowed allosteric transitions in a coupled biochemical oscillator model showing complex dynamic behavior is investigated. When the allosteric transitions are sufficiently fast one can obtain a low-dimensional asymptotic approximation for the dynamics of the species that evolve on a slow time-scale. Such low-dimensional models are common in studies of biological control systems and little attention has, so far, been given to the dynamic effect of the large number of species usually eliminated from more biochemically detailed models. Here we investigate the dynamic effect of explicit inclusion of allosteric transitions having finite time-scales of equilibration. It is found that slowed allosteric transitions suppress complex dynamic modes such a bursting, quasi-periodicity and chaos. The effect arises as the enzyme of consideration becomes trapped in an active state where it is unable to respond to changes in effector concentration on the time-scale necessary to support the modes of complex dynamics. Slow allosteric transitions may be favourable in biological systems in which complex oscillations are not desirable but which, at the same time, may benefit from the presence of positive feedbacks. Our findings suggest that slow allosteric transitions and finite internal rates in general may contribute significantly to the dynamics of biological control mechanisms.

Allosteric Regulation↗
PubMed1993

Flexible effects of quantified cigarette-smoke delivery on EEG dimensional complexity.

A quantified smoke delivery system (QSDS) was used to experimentally control the administration of inhaled cigarette smoke to 28 male smokers. One puff (2 s, 35 cc) was taken every 30 s on a cigarette (nicotine yield 1.0 mg) until the char line reached 3 mm from the filter wrap. The smoke was inhaled for 5 s. Resting eyes-closed and eyes-open EEG was recorded from F3, F4, P3, and P4 before and after quantified smoke delivery (QSD). EEG dimensional complexity (DCx, a measure derived from chaos theory) was computed using the Takens-Ellner method. QSD appeared to have a 'flexible' effect on EEG DCx, primarily lowering it in subjects whose pre-smoking level was high, not affecting it in subjects whose pre-smoking level was intermediate, and tending to raise it in subjects whose pre-smoking level was low. This replicates previous results obtained with ad libitum smoking, suggesting the hypothesis that smoking may have an "optimizing" effect on the complexity of brain dynamics.

Adult↗
PubMed2001

Chaos and regular dynamics in model multi-habitat plankton-fish communities.

This work is focused on the role of diffusive interaction between separate habitats in a patchy environment in plankton pattern formation. We demonstrate that conceptual reaction-diffusion mathematical models constitute an appropriate tool for searching and understanding basic mechanisms of plankton pattern formation and complex spatio-temporal plankton dynamics

Animals↗
PubMed2004

Synchrony & chaos in patchy ecosystems.

The apparent synchronisation of spatially discrete populations is a well documented phenomenon. However, it is not clear what the governing mechanisms are for this synchrony, and whether they are robust over a range of environmental conditions and patch specific population dynamic behaviours. In this paper, we explore two (possibly interacting) modes of coupling, and investigate their theoretically discernible, and perhaps even experimentally measurable, signatures. To aid us in this investigation we employ a planktonic example system, with direct application to plankton patchiness. Furthermore, we address the role of chaos in complex spatio-temporal dynamics; we find that chaos associated with funnel attractors can play a distinguished role, over dynamics less sensitive to small variations, in being more susceptible to generalised synchronisation (such as phase synchronisation) in the presence of small local parameter variation. This is in contrast to the case for coupled systems with identical dynamics, and suggests that non-identically coupled systems are more vulnerable to global extinction events when exhibiting funnel-type chaotic dynamics.

Animals↗
PubMed2005

Kinematic and dynamic processes for the control of pointing movements in humans revealed by short-term exposure to microgravity.

The generation of accurate motor commands requires implicit knowledge of both limb and environmental dynamics. The action of gravity on moving limb segments must be taken into account within the motor command, and may affect the limb trajectory chosen to accomplish a given motor task. Exactly how the CNS deals with these gravitoinertial forces remains an open question. Does the CNS measure gravitational forces directly, or are they accommodated in the motor plan by way of internal models of physical laws? In this study five male subjects participated. We measured kinematic and dynamic parameters of upward and downward arm movements executed at two different speeds, in both normal Earth gravity and in the weightless conditions of parabolic flight. Exposure to microgravity affected velocity profiles for both directions and speeds. The shape of velocity profiles (the ratio of maximum to mean velocity) and movement duration both showed transient perturbations initially in microgravity, but returned to normal gravity values with practice in 0 x g. Differences in relative time to peak velocity between upward versus downward movements, persisted for all trial performed in weightlessness. These differences in kinematic profiles and in the torque profiles used to produce them, diminished, however, with practice in 0 x g. These findings lead to the conclusion that the CNS explicitly represents gravitational and inertial forces in the internal models used to generate and execute arm movements. Furthermore, the results suggest that the CNS adapts motor plans to novel environments on different time scales; dynamics adapt first to reproduce standard kinematics, and then kinematics patterns are adapted to optimize dynamics.

Adult↗
PubMed1996

Characterization of low-dimensional dynamics in the crayfish caudal photoreceptor.

Attempts to detect and characterize chaos in biological systems are of considerable interest, especially in medical science, where successful demonstrations may lead to new diagnostic tools and therapies. Unfortunately, conventional methods for identifying chaos often yield equivocal results when applied to biological data, which are usually heavily contaminated with noise. For such applications, a new technique based on the detection of unstable periodic orbits holds promise. Infinite sets of unstable periodic orbits underlie chaos in dissipative systems; accordingly, the new method searches a time series only for rare events characteristic of these unstable orbits, rather than analysing the structure of the series as a whole. Here we demonstrate the efficacy of the method when applied to the dynamics of the crayfish caudal photoreceptor (subject to stimuli representative of the animal's natural habitat). Our findings confirm the existence of low-dimensional dynamics in the system, and strongly suggest the existence of deterministic chaos. More importantly, these results demonstrate the power of methods based on the detection of unstable periodic orbits for identifying low-dimensional dynamics--and, in particular, chaos--in biological systems.

Action Potentials↗
PubMed2006

Symbolic synchronization and the detection of global properties of coupled dynamics from local information.

We study coupled dynamics on networks using symbolic dynamics. The symbolic dynamics is defined by dividing the state space into a small number of regions (typically 2), and considering the relative frequencies of the transitions between those regions. It turns out that the global qualitative properties of the coupled dynamics can be classified into three different phases based on the synchronization of the variables and the homogeneity of the symbolic dynamics. Of particular interest is the homogeneous unsynchronized phase, where the coupled dynamics is in a chaotic unsynchronized state, but exhibits qualitative similar symbolic dynamics at all the nodes in the network. We refer to this dynamical behavior as symbolic synchronization. In this phase, the local symbolic dynamics of any arbitrarily selected node reflects global properties of the coupled dynamics, such as qualitative behavior of the largest Lyapunov exponent and phase synchronization. This phase depends mainly on the network architecture, and only to a smaller extent on the local chaotic dynamical function. We present results for two model dynamics, iterations of the one-dimensional logistic map and the two-dimensional Henon map, as local dynamical function.

Algorithms↗
PubMed2004

Bifurcations and chaos in a predator-prey system with the Allee effect.

It is known from many theoretical studies that ecological chaos may have numerous significant impacts on the population and community dynamics. Therefore, identification of the factors potentially enhancing or suppressing chaos is a challenging problem. In this paper, we show that chaos can be enhanced by the Allee effect. More specifically, we show by means of computer simulations that in a time-continuous predator-prey system with the Allee effect the temporal population oscillations can become chaotic even when the spatial distribution of the species remains regular. By contrast, in a similar system without the Allee effect, regular species distribution corresponds to periodic/quasi-periodic oscillations. We investigate the routes to chaos and show that in the spatially regular predator-prey system with the Allee effect, chaos appears as a result of series of period-doubling bifurcations. We also show that this system exhibits period-locking behaviour: a small variation of parameters can lead to alternating regular and chaotic dynamics.

Computer Simulation↗
PubMed2002

Fine structures in sheared granular flows.

Computer simulations were used to investigate shear flows of large numbers of viscoelastic, monosized, spherical particles in unbounded and bounded systems with solid fractions ranging from 0.16 to 0.59. A modified hard-sphere model with inelastic, instantaneous particle interactions was found to replicate some results predicted by kinetic theory in an unbounded shear flow at low and moderate solids fractions. This model was found to predict features such as particle lateral diffusive motion even for systems at solid fractions as high as 0.56. However, for higher solid fractions where phenomena such as jamming could occur, a particle dynamics model accounting for particle contacts of finite duration has been developed, in which the viscoelastic behavior of the particles was represented using a nonlinear Hertzian model. The nonlinear viscoelastic model was found to give more reasonable predictions for cluster formation than previously reported linear models, especially when accounting for surface friction in the model. However, neither frictionless nor frictional particle models could predict particle ordering in unbounded flows. As such, simulations were performed for bounded systems using both the modified hard-sphere model and the nonlinear particle dynamic model. For a bounded shear flow, particle ordering could be predicted by the hard-sphere model even in the absence of both particle friction and gravity, with the local solid fraction and wall separation distance governing the flow stability. For these conditions chain formation was found to be quite likely in the disordered layers for frictional particles. The interesting stick-slip dynamics could be clearly observed in the normal stress signal at the bottom wall. Interpretations were proposed for the complex processes observed, which could lay the foundation for further investigations in sheared dense granular systems.

Journal Article↗
PubMed2006

Synchronization in complex networks with a modular structure.

Networks with a community (or modular) structure arise in social and biological sciences. In such a network individuals tend to form local communities, each having dense internal connections. The linkage among the communities is, however, much more sparse. The dynamics on modular networks, for instance synchronization, may be of great social or biological interest. (Here by synchronization we mean some synchronous behavior among the nodes in the network, not, for example, partially synchronous behavior in the network or the synchronizability of the network with some external dynamics.) By using a recent theoretical framework, the master-stability approach originally introduced by Pecora and Carroll in the context of synchronization in coupled nonlinear oscillators, we address synchronization in complex modular networks. We use a prototype model and develop scaling relations for the network synchronizability with respect to variations of some key network structural parameters. Our results indicate that random, long-range links among distant modules is the key to synchronization. As an application we suggest a viable strategy to achieve synchronous behavior in social networks.

Action Potentials↗