Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “Nonlinear Dynamics”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,477 records · Page 82Linked to original sources
PubMed2000

Reconstructing bifurcation diagrams of dynamical systems using measured time series.

We present an algorithm for reconstructing the bifurcation structure of a dynamical system from time series. The method consists in finding a parameterized predictor function whose bifurcation structure is similar to that of the given system. Nonlinear autoregressive (NAR) models with polynomial terms are employed as predictor functions. The appropriate terms in the NAR models are obtained using a fast orthogonal search scheme. This scheme eliminates the problem of multiparameter optimization and makes the approach robust to noise. The algorithm is applied to the reconstruction of the bifurcation diagram (BD) of a neuron model from the simulated membrane potential waveforms. The reconstructed BD captures the different behaviors of the given system. Moreover, the algorithm also works well even for a limited number of time series.

Algorithms↗
PubMed2001

Egg size evolution and energetic constraints on population dynamics.

We use population models that are based on dynamic energy budget models for individuals in order to study the evolution of offspring size and its relationship to the evolution of population dynamics. We show the existence of alternative evolutionarily stable strategies for offspring investment strategy resulting from a trade off between offspring number and time-to-maturity. The model predicts egg energy in Daphnia magna well, and suggests that the observed egg energy in D. magna is the result of selection for minimal egg investment constrained by minimum viable egg energy, combined with selection for a juvenile energy reserve. The selection for minimal egg size pushes populations toward chaotic dynamics. However, the minimum viable egg size combined with low efficiency of conversion of energy to new biomass is sufficient to keep population dynamics out of chaos.

Animals↗
PubMed2003

Unbiased rotational moves for rigid-body dynamics.

We introduce an unbiased protocol for performing rotational moves in rigid-body dynamics simulations. This approach-based on the analytic solution for the rotational equations of motion for an orthogonal coordinate system at constant angular velocity-removes deficiencies that have been largely ignored in Brownian dynamics simulations, namely errors for finite rotations that result from applying the noncommuting rotational matrices in an arbitrary order. Our algorithm should thus replace standard approaches to rotate local coordinate frames in Langevin and Brownian dynamics simulations.

Algorithms↗
PubMed2002

Reconfigurable control system design for fault diagnosis and accommodation.

The growing demand in system reliability and survivability under failures has urged ever-increasing research effort on the development of fault diagnosis and accommodation. In this paper, the on-line fault tolerant control problem for dynamic systems under unanticipated failures is investigated from a realistic point of view without any specific assumption on the type of system dynamical structure or failure scenarios. The sufficient conditions for system on-line stability under catastrophic failures have been derived using the discrete-time Lyapunov stability theory. Based upon the existing control theory and the modern computational intelligence techniques, an on-line fault accommodation control strategy is proposed to deal with the desired trajectory-tracking problems for systems suffering from various unknown and unanticipated catastrophic component failures. Theoretical analysis indicates that the control problem of interest can be solved on-line without a complete realization of the unknown failure dynamics provided an on-line estimator satisfies certain conditions. Through the on-line estimator, effective control signals to accommodate the dynamic failures can be computed using only the partially available information of the faults. Several on-line simulation studies have been presented to demonstrate the effectiveness of the proposed strategy. To investigate the feasibility of using the developed technique for unanticipated fault accommodation in hardware under the real-time environment, an on-line fault tolerant control test bed has been constructed to validate the proposed technology. Both on-line simulations and the real-time experiment show encouraging results and promising futures of on-line real-time fault tolerant control based solely upon insufficient information of the system dynamics and the failure dynamics.

Computer Systems↗
PubMed1996

A new type of self-organization associated with chaotic dynamics in neural networks.

A new type of self-organized dynamics is presented, in relation with chaos in neural networks. One is chaotic itinerancy and the other is chaos-driven contraction dynamics. The former is addressed as a universal behavior in high-dimensional dynamical systems. In particular, it can be viewed as one possible form of memory dynamics in brain. The latter gives rise to singular-continuous nowhere-differentiable attractors. These dynamics can be related to each other in the context of dimensionality and of chaotic information processings. Possible roles of these complex dynamics in brain are also discussed.

Animals↗
PubMed2004

A solution for two-dimensional mazes with use of chaotic dynamics in a recurrent neural network model.

Chaotic dynamics introduced into a neural network model is applied to solving two-dimensional mazes, which are ill-posed problems. A moving object moves from the position at t to t + 1 by simply defined motion function calculated from firing patterns of the neural network model at each time step t. We have embedded several prototype attractors that correspond to the simple motion of the object orienting toward several directions in two-dimensional space in our neural network model. Introducing chaotic dynamics into the network gives outputs sampled from intermediate state points between embedded attractors in a state space, and these dynamics enable the object to move in various directions. System parameter switching between a chaotic and an attractor regime in the state space of the neural network enables the object to move to a set target in a two-dimensional maze. Results of computer simulations show that the success rate for this method over 300 trials is higher than that of random walk. To investigate why the proposed method gives better performance, we calculate and discuss statistical data with respect to dynamical structure.

Artificial Intelligence↗
PubMed2004

Real-time computation at the edge of chaos in recurrent neural networks.

Depending on the connectivity, recurrent networks of simple computational units can show very different types of dynamics, ranging from totally ordered to chaotic. We analyze how the type of dynamics (ordered or chaotic) exhibited by randomly connected networks of threshold gates driven by a time-varying input signal depends on the parameters describing the distribution of the connectivity matrix. In particular, we calculate the critical boundary in parameter space where the transition from ordered to chaotic dynamics takes place. Employing a recently developed framework for analyzing real-time computations, we show that only near the critical boundary can such networks perform complex computations on time series. Hence, this result strongly supports conjectures that dynamical systems that are capable of doing complex computational tasks should operate near the edge of chaos, that is, the transition from ordered to chaotic dynamics.

Animals↗
PubMed2005

What can a neuron learn with spike-timing-dependent plasticity?

Spiking neurons are very flexible computational modules, which can implement with different values of their adjustable synaptic parameters an enormous variety of different transformations F from input spike trains to output spike trains. We examine in this letter the question to what extent a spiking neuron with biologically realistic models for dynamic synapses can be taught via spike-timing-dependent plasticity (STDP) to implement a given transformation F. We consider a supervised learning paradigm where during training, the output of the neuron is clamped to the target signal (teacher forcing). The well-known perceptron convergence theorem asserts the convergence of a simple supervised learning algorithm for drastically simplified neuron models (McCulloch-Pitts neurons). We show that in contrast to the perceptron convergence theorem, no theoretical guarantee can be given for the convergence of STDP with teacher forcing that holds for arbitrary input spike patterns. On the other hand, we prove that average case versions of the perceptron convergence theorem hold for STDP in the case of uncorrelated and correlated Poisson input spike trains and simple models for spiking neurons. For a wide class of cross-correlation functions of the input spike trains, the resulting necessary and sufficient condition can be formulated in terms of linear separability, analogously as the well-known condition of learnability by perceptrons. However, the linear separability criterion has to be applied here to the columns of the correlation matrix of the Poisson input. We demonstrate through extensive computer simulations that the theoretically predicted convergence of STDP with teacher forcing also holds for more realistic models for neurons, dynamic synapses, and more general input distributions. In addition, we show through computer simulations that these positive learning results hold not only for the common interpretation of STDP, where STDP changes the weights of synapses, but also for a more realistic interpretation suggested by experimental data where STDP modulates the initial release probability of dynamic synapses.

Action Potentials↗
PubMed2000

Modeling of dose-response-time data: four examples of estimating the turnover parameters and generating kinetic functions from response profiles.

The most common approach to in vivo pharmacokinetic and pharmacodynamic modeling involves sequential analysis of the plasma concentration versus time and then response versus time data, such that the plasma kinetic model provides an independent function, driving the dynamics. However, response versus time data, even in the absence of measured drug concentrations, inherently contain useful information about the turnover characteristics of response (turnover rate, half-life of response), the drug's biophase kinetics (F, half-life) as well as the pharmacodynamic characteristics (potency, intrinsic activity). Previous analyses have assumed linear kinetics, linear dynamics, no time lag between kinetics and dynamics (single-valued response), and time constant parameters. However, this report demonstrates that the drug effect can be indirect (antinociception, cortisol/adrenocorticotropin (ACTH), body temperature), display nonlinear kinetics, display feedback mechanisms (nonstationarity, cortiso/ACTH) and exhibit hysteresis with the drug levels in the biophase (antinociception, body temperature). It is also demonstrated that crucial determinants of the success of modeling dose-response-time data are the dose selection, multiple dosing, and to some extent different input rates and routes. This report exemplifies the possibility of assigning kinetic forcing functions in pharmacodynamic modeling in both preclinical and clinical studies for the purpose of characterizing (discrimination between turnover and drug-specific parameters) response data and optimizing subsequent clinical protocols, and for identification of inter-individual differences.

Animals↗
PubMed1994

Non-linear dynamical analysis of multichannel EEG: clinical applications in dementia and Parkinson's disease.

The irregular, aperiodic character of the EEG is usually explained by a stochastic model. In this view the EEG is linearly filtered noise. According to chaos theory such irregular signals can also result from low dimensional deterministic chaos. In this case the underlying dynamics is nonlinear, and has only few effective degrees of freedom. In contrast, stochastic models are less efficient, because they require in principle infinite degrees of freedom. Chaotic dynamics in the EEG can be studied by calculating the correlation dimension (D2). Although it has become clear that D2 calculations alone cannot prove chaos, the D2 has potential value as an EEG diagnostic. In this study we investigated whether D2 could be used to discriminate EEGs from normal controls, demented patients and Parkinson patients. We have analyzed epochs (20 channels; 2.5 s) from 52 EEGs (20 controls; 15 patients with dementia; 17 patients with Parkinson's disease). Controls had a mean D2 of 6.5 (0.9); demented patients of 4.4 (1.5), and Parkinson patients of 5.3 (0.9). Both groups were significantly different from controls (p < 0.001). There was a significant positive correlation between D2 and relative power in the beta band (r = 0.81) and a significant negative correlation between D2 and power in the delta (r = -0.60) and theta band (r = -0.37). These results suggest the possible usefulness of multichannel D2 estimation in a clinical setting.

Aged↗
PubMed2004

Excitable dynamics and threshold sets in nonlinear systems.

Following our previous work [J. Zagora et al., Faraday Discuss. 120, 313 (2001)], we present a quantitative definition of a threshold that separates large-amplitude excitatory responses and small-amplitude nonexcitatory responses to a perturbation of an excitable system with a single globally attracting steady state. For systems with two variables, finding the threshold set is formulated as a boundary value problem supplemented by a condition of a maximum separation rate. For this highly nonlinear problem we formulate a numerical method based on the use of multiple shooting and continuation methods. The threshold phenomena are examined by using an example dynamical system with chemical reaction--the bromate-sulfite-ferrocyanide system. In a model of this reaction we find the threshold set, construct a bifurcation diagram and discuss how excitability can vanish. These results are compared with recent experiments. We also discuss relevance of other definitions of the excitability threshold including the concept of nullclines.

Journal Article↗
PubMed1997

Measurement and simulation of water transport during freezing in mammalian liver tissue.

Optimization of cryosurgical procedures on deep tissues such as liver requires an increased understanding of the fundamental mechanisms of ice formation and water transport in tissues during freezing. In order to further investigate and quantify the amount of water transport that occurs during freezing in tissue, this study reports quantitative and dynamic experimental data and theoretical modeling of rat liver freezing under controlled conditions. The rat liver was frozen by one of four methods of cooling: Method 1-ultrarapid "slam cooling" (> or = 1000 degrees C/min) for control samples; Method 2-equilibrium freezing achieved by equilibrating tissue at different subzero temperatures (-4, -6, -8, -10 degrees C); Method 3-two-step freezing, which involves cooling at 5 degrees C/min. to -4, -6, -8, -10 or -20 degrees C followed immediately by slam cooling; or Method 4-constant and controlled freezing at rates from 5-400 degrees C/min. on a directional cooling stage. After freezing, the tissue was freeze substituted, embedded in resin, sectioned, stained, and imaged under a light microscope fitted with a digitizing system. Image analysis techniques were then used to determine the relative cellular to extracellular volumes of the tissue. The osmotically inactive cell volume was determined to be 0.35 by constructing a Boyle van't Hoff plot using cellular volumes from Method 2. The dynamic volume of the rat liver cells during cooling was obtained using cellular volumes from Method 3 (two-step freezing at 5 degrees C/min). A nonlinear regression fit of a Krogh cylinder model to the volumetric shrinkage data in Method 3 yielded the biophysical parameters of water transport in rat liver tissue of: Lpg = 3.1 x 10(-13) m3/Ns (1.86 microns/min-atm) and ELp = 290 kJ/mole (69.3 kcal/mole), with chi-squared variance of 0.00124. These parameters were then incorporated into the Krogh cylinder model and used to simulate water transport in rat liver tissue during constant cooling at rates between 5-100 degrees C/min. Reasonable agreement between these simulations and the constant cooling rate freezing experiments in Method 4 were obtained. The model predicts that the water transport ceases at a relatively high subzero temperature (-10 degrees C), such that the amount of intracellular ice forming in the tissue cells rises from almost none (= extensive dehydration and vascular expansion) at < or = 5 degrees C/min to over 88 percent of the original cellular water at > or = 50 degrees C/min. The theoretical simulations based on these experimental methods may be of use in visualizing and predicting freezing response, and thus can assist in the planning and implementing of cryosurgical protocols.

Animals↗
PubMed2005

Refractory periods and climate forcing in cholera dynamics.

Outbreaks of many infectious diseases, including cholera, malaria and dengue, vary over characteristic periods longer than 1 year. Evidence that climate variability drives these interannual cycles has been highly controversial, chiefly because it is difficult to isolate the contribution of environmental forcing while taking into account nonlinear epidemiological dynamics generated by mechanisms such as host immunity. Here we show that a critical interplay of environmental forcing, specifically climate variability, and temporary immunity explains the interannual disease cycles present in a four-decade cholera time series from Matlab, Bangladesh. We reconstruct the transmission rate, the key epidemiological parameter affected by extrinsic forcing, over time for the predominant strain (El Tor) with a nonlinear population model that permits a contributing effect of intrinsic immunity. Transmission shows clear interannual variability with a strong correspondence to climate patterns at long periods (over 7 years, for monsoon rains and Brahmaputra river discharge) and at shorter periods (under 7 years, for flood extent in Bangladesh, sea surface temperatures in the Bay of Bengal and the El Niño-Southern Oscillation). The importance of the interplay between extrinsic and intrinsic factors in determining disease dynamics is illustrated during refractory periods, when population susceptibility levels are low as the result of immunity and the size of cholera outbreaks only weakly reflects climate forcing.

Bangladesh↗
PubMed2005

Dynamical behaviour of epidemiological models with sub-optimal immunity and nonlinear incidence.

In this paper we analyze the dynamics of two families of epidemiological models which correspond to transitions from the SIR (susceptible-infectious-resistant) to the SIS (susceptible-infectious-susceptible) frameworks. In these models we assume that the force of infection is a nonlinear function of density of infectious individuals, I. Conditions for the existence of backwards bifurcations, oscillations and Bogdanov-Takens points are given.

Communicable Diseases↗