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PubMed2004

Power controlled soliton stability and steering in lattices with saturable nonlinearity.

Dynamical properties of discrete solitons in nonlinear Schrödinger lattices with saturable nonlinearity are studied in the framework of the one-dimensional discrete Vinetskii-Kukhtarev model. Two stationary strongly localized modes, centered on site (A) and between two neighboring sites (B), are obtained. The associated Peierls-Nabarro potential is bounded and has multiple zeros indicating strong implications on the stability and dynamics of the localized modes. Besides a stable propagation of mode A, a stable propagation of mode B is also possible. The enhanced ability of the large power solitons to move across the lattice is pointed out and numerically verified.

Journal Article↗

PubMed2004

A new view on visuomotor channels: the case of the disappearing dynamics.

A considerable body of kinematic data supports the proposal that independent visuomotor channels are involved in the control of the transport and grip components of reach and grasp. These channels are seen as having separate perceptual inputs, outputs and internal processing and are thought by some to correspond to independent neuroanatomical pathways. The idea that different groups of muscles and biomechanical structures can be controlled independently is attractive, but this kinematically-inspired hypothesis fails to take into account the complexity of the dynamic relationships and their interactions within the neuromusculoskeletal system. Inertial, viscous, centrifugal, coriolis, gravitational and reflex cross couplings exist between efferent drives to muscles and resulting body movements. Rotation at even a single joint generates a complex set of dynamic reaction forces and requires coordinated activation of many muscles throughout the body to maintain posture and balance. In this theoretical paper we present a new view of independent visuomotor channels in the form of an adaptive neural controller that can compensate for the above interactions and decouple the relationships between efferent drives to muscles and resulting body movements. At the same time, the neural controller renders all the dynamics (linear and nonlinear), other than time delays, of the neuromusculoskeletal system, unobservable in the visuomotor relationships. Using the geometry of nonlinear dynamical systems we show that, providing certain constraints on the structure of time delays within the system are satisfied, there exists a neural controller that can render all the dynamics of the neuromusculoskeletal system (except for time delays) unobservable in the responses. The controller simultaneously decouples all the interactive dynamics so that each of the m independent inputs controls one and only one degree of freedom of the response. This means that each degree of freedom in a multi-joint response can be controlled by an independent component of the visual input, a behaviour that has long been observed in visual tracking experiments. The controller effectively establishes m independent visuomotor channels. However, rather than reflecting separate neuroanatomical pathways, the independent channels result from a neural controller with convergent and divergent connections to compensate for the interactive nonlinear dynamics within the neuromusculoskeletal system. This new view of visuomotor channels has implications for neural control processes involved in the acquisition and adaptability of skilled perceptual-motor behaviour in general, as well as for the design of robotic controllers.

Biomechanical Phenomena↗

PubMed2006

Nonlinear model dynamics for closed-system, constrained, maximal-entropy-generation relaxation by energy redistribution.

We discuss a nonlinear model for relaxation by energy redistribution within an isolated, closed system composed of noninteracting identical particles with energy levels with . The time-dependent occupation probabilities are assumed to obey the nonlinear rate equations where and are functionals of the 's that maintain invariant the mean energy and the normalization condition . The entropy is a nondecreasing function of time until the initially nonzero occupation probabilities reach a Boltzmann-like canonical distribution over the occupied energy eigenstates. Initially zero occupation probabilities, instead, remain zero at all times. The solutions of the rate equations are unique and well defined for arbitrary initial conditions and for all times. The existence and uniqueness both forward and backward in time allows the reconstruction of the ancestral or primordial lowest entropy state. By casting the rate equations in terms not of the 's but of their positive square roots , they unfold from the assumption that time evolution is at all times along the local direction of steepest entropy ascent or, equivalently, of maximal entropy generation. These rate equations have the same mathematical structure and basic features as the nonlinear dynamical equation proposed in a series of papers ending with G. P. Beretta, Found. Phys. 17, 365 (1987) and recently rediscovered by S. Gheorghiu-Svirschevski [Phys. Rev. A 63, 022105 (2001);63, 054102 (2001)]. Numerical results illustrate the features of the dynamics and the differences from the rate equations recently considered for the same problem by M. Lemanska and Z. Jaeger [Physica D 170, 72 (2002)]. We also interpret the functionals and as nonequilibrium generalizations of the thermodynamic-equilibrium Massieu characteristic function and inverse temperature, respectively.

Journal Article↗

PubMed2001

Nonlinear EEG dynamics during imagined self-paced movements.

The majority of studies devoted to reveal electrophysiological correlates of words and sentences comprehension, imageability and remembering are based on the event-related potentials and frequency synchronization in different narrow frequency bands. These linear methods reveal some patterns of EEG activity in time and frequency domain. Having in mind that the activation of many cortical structures is a result of mass of nonlinearly interconnected neurons, the linear methods seem to be insufficient to discover the complexity of the information transfer. We revealed recently nonlinear dynamic transients in EEG, long before real performance of goal-directed voluntary movements with different temporal and spatial distributions over frontal, sensorimotor and parietal cortical areas (Popivanov and Dushanova, 1999). The aim of this study was to establish whether similar behavior of the nonlinear characteristics exists when the subject imagines movements of a given type. The Kolmogorov entropy computed over time after the sentence end proved to be an useful characteristic that complement the linear methods.

Eidetic Imagery↗

PubMed1989

Paraplegic standing controlled by functional neuromuscular stimulation: Part I--computer model and control-system design.

We have developed a planar computer model to investigate paraplegic standing induced by functional neuromuscular stimulation. The model consists of nonlinear musculotendon dynamics (pulse train activation dynamics and musculotendon actuator dynamics), nonlinear body-segmental dynamics, and a linear output-feedback control law. The model of activation dynamics is an analytic expression that characterizes the relation between the stimulus parameters (pulse width and interpulse interval) and the muscle activation. Hill's classic two-element muscle model was modified into a musculotendon actuator model in order to account for the effects of submaximal activation and tendon elasticity on development of force by the actuator. The three body-segmental, multijoint model accounts for the anterior-posterior movements of the head and trunk, the thigh, and the shank. We modeled arm movement as an external disturbance and imposed the disturbance to the body-segmental dynamics by means of a quasistatic analysis. Linearization, and at times linear approximation of the computer model, enabled us to compute a constant, linear feedback-gain matrix, whose output is the net activation needed by a dynamical joint-torque actuator. Motivated by an assumption that minimization of energy expenditure lessens muscle fatigue, we developed an algorithm that then computes how to distribute the net activation among all the muscles crossing the joint. In part II, the combined feedback control strategy is applied to the nonlinear model of musculotendon and body-segmental dynamics to study how well the body ought to maintain balance should the feedback control strategy be employed.

Biomechanical Phenomena↗

PubMed1994

Psychiatry and the new dynamics.

Self-organizing and self-tuning neural networks are conceptualized as nonlinear dynamical systems. It is shown that biological psychiatry can be encompassed within this nonlinear dynamical framework, where it becomes coherent with trends in cognitive science. A state space representation that is a hyperspace with an energy topology and a fractal dimension is utilized. The state space representation provides a unifying framework for the classification of mental disorders. Clinical phenomena in schizophrenia can be explained in terms of nonlinear dynamics. The framework is also productive of psychiatric research. These results motivate the development of a nonlinear dynamical psychiatry.

Autistic Disorder↗

PubMed2003

Nonlinear polarization dynamics in directly modulated vertical-cavity surface-emitting lasers.

A current-modulated vertical-cavity surface-emitting laser is shown to exhibit interesting nonlinear dynamics in its two orthogonal linearly polarized (LP), fundamental transverse modes. The intensities of the two LP modes may exhibit in-phase time-periodic dynamics or chaotic regimes with combination of in-phase and antiphase dynamics at two different time scales. Chaotic dynamics are found in a large range of laser and modulation parameters.

Journal Article↗

PubMed1994

Chaos and physiology: deterministic chaos in excitable cell assemblies.

In this review we examined the emerging science of deterministic chaos (nonlinear systems theory) and its application to selected physiological systems. Although many of the popular images of fractals represent fascination and beauty that by analogy corresponds to nature as we see it, the question remains as to its ultimate meaning for physiological processes. It was our intent to help clarify this somewhat popular, somewhat obscure area of nonlinear dynamics in the context of an ever-changing procedural base. We examined not only the basic concepts of chaos, but also its applications ranging from observations in single cells to the complexity of the EEG. We have not suggested that nonlinear dynamics will answer all of our questions; however, we did attempt to illustrate ways in which this approach may help us to answer new questions and to rearticulate old ones. Chaos is revolutionary in that the overall approach requires us to adopt a different frame of reference which, at times, may move us away from previous concerns and methods of data analysis. In sections I-IV, we summarized the nonlinear dynamics approach and described its application to physiology and neural systems. First, we presented a general overview of the application of nonlinear dynamical techniques to neural systems. We discussed the manner in which even apparently simple deterministic systems can behave in an unpredictable manner. Second, we described the principles of nonlinear dynamical systems including the derived analytical techniques. We now see a variety of procedures for delineating whether frenetic chaotic behavior results from a nonlinear dynamical system with a few degrees of freedom, or whether it is caused by an infinite number of variables, i.e., noise. Third, we approached the applications of nonlinear procedures to the cardiovascular systems and to the neurosciences. In terms of time series, we described initial studies which applied the now "traditional" measures of dimensionality (e.g., based on the algorithm by Grassberger and Procaccia) and information change (e.g., Lyapunov exponents). Examples include our own work and that of Pritchard et al., demonstrating that the dynamics of neural mass activity reflect psychopathological states. Today, however, the trend has expanded to include the use of surrogate data and statistical null hypotheses testing to examine whether a given time series can be considered different from that of white or colored noise (cf. Ref. 262). One of the most important potential applications is that of quantifying changes in nonlinear dynamics to predict future states of the system.(ABSTRACT TRUNCATED AT 400 WORDS)

Animals↗

PubMed2002

Nonlinear analysis of irregular animal vocalizations.

Animal vocalizations range from almost periodic vocal-fold vibration to completely atonal turbulent noise. Between these two extremes, a variety of nonlinear dynamics such as limit cycles, subharmonics, biphonation, and chaotic episodes have been recently observed. These observations imply possible functional roles of nonlinear dynamics in animal acoustic communication. Nonlinear dynamics may also provide insight into the degree to which detailed features of vocalizations are under close neural control, as opposed to more directly reflecting biomechanical properties of the vibrating vocal folds themselves. So far, nonlinear dynamical structures of animal voices have been mainly studied with spectrograms. In this study, the deterministic versus stochastic (DVS) prediction technique was used to quantify the amount of nonlinearity in three animal vocalizations: macaque screams, piglet screams, and dog barks. Results showed that in vocalizations with pronounced harmonic components (adult macaque screams, certain piglet screams, and dog barks), deterministic nonlinear prediction was clearly more powerful than stochastic linear prediction. The difference, termed low-dimensional nonlinearity measure (LNM), indicates the presence of a low-dimensional attractor. In highly irregular signals such as juvenile macaque screams, piglet screams, and some dog barks, the detectable amount of nonlinearity was comparatively small. Analyzing 120 samples of dog barks, it was further shown that the harmonic-to-noise ratio (HNR) was positively correlated with LNM. It is concluded that nonlinear analysis is primarily useful in animal vocalizations with strong harmonic components (including subharmonics and biphonation) or low-dimensional chaos.

Animals↗

PubMed2003

Substance abuse as a dynamical disease: evidence and clinical implications of nonlinearity in a time series of daily alcohol consumption.

Several authors have suggested that chaos theory, the study of nonlinear dynamics and the application of the knowledge gained to natural and social phenomena, might yield insight into substance-related disorders. In this article, we examine the dynamics of substance abuse by fitting a nonlinear model to a time series of the amount of alcohol, which an adult male with a diagnosis of substance abuse consumed on a daily basis. The nonlinear model shows a statistically superior fit when compared to a linear model. We then use the model to explore a question that is pertinent to the treatment of substance abuse, whether controlled drinking or abstinence is a preferred strategy for maintaining sobriety.

Adult↗

PubMed1995

Dynamic viscoelastic nonlinearity of lung parenchymal tissue.

To investigate the contribution of nonlinear tissue viscoelasticity to the dynamic behavior of lung, time and frequency responses of isolated parenchymal strips of degassed dog lungs were investigated. The strips were subjected to loading and unloading stretch steps for 60 s and to sinusoidal oscillations (0.03-3 Hz) of different stretch amplitudes (delta lambda = 0.05, 0.1, and 0.2) and at different operating stresses (T(o) = 0.5, 1, and 2 kPa). Elastance (E) increased linearly with the logarithm of frequency (approximately 10% per frequency decade), and resistance (R) decreased hyperbolically with frequency. Both E and R varied little with delta lambda but they increased proportionally with T(o). Hysteresivity (eta = R x 2 pi x frequency/E) ranged from 0.07 to 0.10. In agreement with the frequency response, the magnitude of the unit step response increased with T(o) and was higher when loading than when unloading, and the stress relaxation ratio (approximately 0.10) did not vary greatly with T(o) or with delta lambda. The time and frequency behavior of the strips were interpreted in terms of the quasilinear viscoelastic model of Navajas et al. (J. Appl. Physiol. 73:2681-2692, 1992). The model explains most of the dependencies of step and oscillatory responses on the measurement conditions, in particular the proportional dependence of E and R on T(o). According to the model, about two-thirds of energy dissipated during oscillation arises from tissue viscoelasticity. The remaining dissipated energy could be accounted for by plasticity. Thus the effect of nonlinear elasticity on the dynamic behavior of lung tissue can be empirically described by a simple quasilinear model characterized by only two parameters.

Animals↗

PubMed1994

The ecological effects of individual exposures and nonlinear disease dynamics in populations.

To describe causally predictive relationships, model parameters and the data used to estimate them must correspond to the social context of causal actions. Causes may act directly upon the individual, during a contact between individuals, or upon a group dynamic. Assuming that outcomes in different individuals are independent puts the causal action directly upon individuals. Analyses making this assumption are thus inappropriate for infectious diseases, for which risk factors alter the outcome of contacts between individuals. Transmission during contact generates nonlinear infection dynamics. These dynamics can so attenuate exposure-infection relationships at the individual level that even risk factors causing the vast majority of infections can be missed by individual-level analyses. On the other hand, these dynamics amplify causal associations between exposure and infection at the ecological level. The amplification and attenuation derive from chains of transmission initiated by exposed individuals but involving unexposed individuals. A study of household exposure to the only vector of dengue in Mexico illustrates the phenomenon. An individual-level analysis demonstrated almost no association between exposure and infection. Ecological analysis, in contrast, demonstrated a strong association. Transmission models that are devoid of any sources of the ecological fallacy are used to illustrate how nonlinear dynamics generate such results.

Dengue↗

PubMed2001

Computation of a stabilizing set of feedback matrices of a large-scale nonlinear musculoskeletal dynamic model.

The purpose of this study is to present a general mathematical framework to compute a set of feedback matrices which stabilize an unstable nonlinear anthropomorphic musculoskeletal dynamic model. This method is activity specific and involves four fundamental stages. First, from muscle activation data (input) and motion degrees-of-freedom (output) a dynamic experimental model is obtained using system identification schemes. Second, a nonlinear musculoskeletal dynamic model which contains the same number of muscles and degrees-of-freedom and best represents the activity being considered is proposed. Third, the nonlinear musculoskeletal model (anthropomorphic model) is replaced by a family of linear systems, parameterized by the same set of input/output data (nominal points) used in the identification of the experimental model. Finally, a set of stabilizing output feedback matrices, parameterized again by the same set of nominal points, is computed such that when combined with the anthropomorphic model, the combined system resembles the structural form of the experimental model. The method is illustrated in regard to the human squat activity.

Adult↗

PubMedDate not supplied

Evidence of deterministic chaos in the myoelectric signal.

Our aim was to study whether the myoelectric signals can be better modelled as outputs of a nonlinear dynamic system rather than as random stochastic signals. Both the nonlinear predictability and the dimensionality of the signals were studied using methods of nonlinear dynamics. The signals were measured from the biceps brachii muscle during both fatiguing and non-fatiguing isometric contractions at low load levels. The myoelectric signals were found to be nonlinear and to have a structure statistically distinguishable from random noise. The correlation dimension describing the dimensionality of the myoelectric signal decreased during local muscular fatigue. The results support the use of the theory of nonlinear dynamics for the modelling of the myoelectric signals.

Adult↗

PubMed1993

A nonlinear perspective in understanding the neurodynamics of EEG.

The developments in nonlinear dynamics and the theory of chaos have considerably altered our perception and analysis of many complex systems, including the brain. This paper reviews the physical and dynamical aspect of brain's electrical activity from this new perspective and indicates possible future directions. The importance of emerging trends of nonlinear dynamics and chaos to neurobiology has been discussed in the context of various states of consciousness and behaviour. In the past, EEG analysis has been confined to descriptive stochastic statistics and any understanding of the transitional process of brain activities was either nonexistent or not amenable for investigation. With the developments in nonlinear dynamics, the chaotic dynamical parameters and trajectory behaviour will find their use as feature detection techniques in EEG. Furthermore, nonlinear dynamics provides a model for EEG generation and temporal prediction which will help in determining the nature of neuronal processes governing various states of brain activity. The formalism of globally coupled dynamic systems will find applications in modelling the transitional states of EEG.

Brain↗

PubMed2006

Towards systemic theories in biological psychiatry.

Although still rather controversial, empirical data on the neurobiology of schizophrenia have reached a degree of complexity that makes it hard to obtain a coherent picture of the malfunctions of the brain in schizophrenia. Theoretical neuropsychiatry should therefore use the tools of theoretical sciences like cybernetics, informatics, computational neuroscience or systems science. The methodology of systems science permits the modeling of complex dynamic nonlinear systems. Such procedures might help us to understand brain functions and the disorders and actions of psychiatric drugs better.

Antipsychotic Agents↗

PubMed2002

Fractal structures of normal and anomalous diffusion in nonlinear nonhyperbolic dynamical systems.

A paradigmatic nonhyperbolic dynamical system exhibiting deterministic diffusion is the smooth nonlinear climbing sine map. We find that this map generates fractal hierarchies of normal and anomalous diffusive regions as functions of the control parameter. The measure of these self-similar sets is positive, parameter dependent, and in case of normal diffusion it shows a fractal diffusion coefficient. By using a Green-Kubo formula we link these fractal structures to the nonlinear microscopic dynamics in terms of fractal Takagi-like functions.

Journal Article↗

PubMed2003

Temporal dynamics of binocular disparity processing in the central visual pathway.

To solve the stereo correspondence problem (i.e., find the matching features of a visual scene in both eyes), it is advantageous to combine information across spatial scales. The details of how this is accomplished are not clear. Psychophysical studies and mathematical models have suggested various types of interactions across spatial scale, including coarse to fine, fine to coarse, averaging, and population coding. In this study, we investigate dynamic changes in disparity tuning of simple and complex cells in the cat's striate cortex over a short time span. We find that disparity frequency increases and disparity ranges decrease while optimal disparity remains constant, and this conforms to a coarse-to-fine mechanism. We explore the origin of this mechanism by examining the frequency and size dynamics exhibited by binocular simple cells and neurons in the lateral geniculate nucleus (LGN). The results suggest a strong role for a feed-forward mechanism, which could originate in the retina. However, we find that the dynamic changes seen in the disparity range of simple cells cannot be predicted from their left and right eye monocular receptive field (RF) size changes. This discrepancy suggests the possibility of a dynamic nonlinearity or disparity specific feedback that alters tuning or a combination of both mechanisms.

Animals↗