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At least 1,423 records · Page 79Linked to original sources
PubMed1999

Non-linear time series analysis of intracranial EEG recordings in patients with epilepsy--an overview.

Deterministic chaos offers a striking explanation for apparently irregular behavior, a characteristic feature of brain electrical activity. The framework of the theory of non-linear dynamics provides new concepts and powerful algorithms to analyze such time series. However, different influencing factors render the use of non-linear measures in a strict sense problematic. Nevertheless, if interpreted with care, particularly the correlation dimension or the Lyapunov-exponents provide a means to reliably characterize different states of normal and pathological brain function. This overview summarizes recent findings applying this concept in the field of epileptology that promise to be important for clinical practice. Non-linear measures extracted from the intra-cranially recorded EEG allow (a) localization of epileptogenic areas in different cerebral regions even during seizure-free intervals, (b) investigation of the influence of anticonvulsive drugs and (c) detection of features predictive of imminent seizure activity. Moreover, particularly the dimensional complexity proves a valuable parameter reflecting spatially distributed neuronal activity during verbal learning and memory processes. Specific changes in time of this non-linear measure allow the prediction of memory performance and, in addition, represent an estimate of the recruitment potency in the anterior mesial temporal lobes. Thus, the application of non-linear time series analysis to brain electrical activity offers new information about the dynamics of the underlying neuronal networks.

Electroencephalography↗
PubMed1998

Is dynamical systems modeling just curve fitting?

The development of mathematical tools for describing dynamical systems has made it possible to characterize forms of behavior that could not be characterized before. This represents progress, but the enterprise runs the risk of being nothing more than curve fitting if investigators fail to identify the physical, biological, or psychological mechanisms which are common to systems that follow the same dynamical regime and which are not common to systems that do not follow the same dynamical regime.

Biomechanical Phenomena↗
PubMed2002

Transient dynamics and pattern formation: reactivity is necessary for Turing instabilities.

The theory of spatial pattern formation via Turing bifurcations - wherein an equilibrium of a nonlinear system is asymptotically stable in the absence of dispersal but unstable in the presence of dispersal - plays an important role in biology, chemistry and physics. It is an asymptotic theory, concerned with the long-term behavior of perturbations. In contrast, the concept of reactivity describes the short-term transient behavior of perturbations to an asymptotically stable equilibrium. In this article we show that there is a connection between these two seemingly disparate concepts. In particular, we show that reactivity is necessary for Turing instability in multispecies systems of reaction-diffusion equations, integrodifference equations, coupled map lattices, and systems of ordinary differential equations.

Animals↗
PubMed2002

Nonlinear optical characterization of cluster dynamic in water in oil microemulsion by a pump probe laser beam technique.

We present a new pump probe laser beams configuration for the nonlinear optical characterization of microemulsions. We detect the variation of the on-axis optical intensity of the probe beam as generated by the concentration profile induced in an optically thin film of microemulsion by the pump beam. A mathematical model has been introduced to describe the phenomenon. The technique allows the determination of both Kerr-like optical nonlinearity and time constants and, therefore, it gives information both on cluster dimension and their shape. We discuss its application to WAD (water/AOT/decane, where AOT denotes sodium-bis-di-ethyl-sulfosuccinate) with the application of a strong electric field of optical source. Comparison between theoretical predictions and experimental results confirms the presence of giant optical nonlinearity in the absence of turbidity divergence. Chainlike shape of clusters, of the kind already reported with the application of strong electric field, could justify this result.

Journal Article↗
PubMed1998

Global identifiability of linear compartmental models--a computer algebra algorithm.

A priori global identifiability deals with the uniqueness of the solution for the unknown parameters of a model and is, thus, a prerequisite for parameter estimation of biological dynamic models. Global identifiability is however difficult to test, since it requires solving a system of algebraic nonlinear equations which increases both in nonlinearity degree and number of terms and unknowns with increasing model order. In this paper, a computer algebra tool, GLOBI (GLOBal Identifiability) is presented, which combines the topological transfer function method with the Buchberger algorithm, to test global identifiability of linear compartmental models. GLOBI allows for the automatic testing of a priori global identifiability of general structure compartmental models from general multi input-multi output experiments. Examples of usage of GLOBI to analyze a priori global identifiability of some complex biological compartmental models are provided.

Algorithms↗
PubMed2001

Real-Time linux dynamic clamp: a fast and flexible way to construct virtual ion channels in living cells.

We describe a system for real-time control of biological and other experiments. This device, based around the Real-Time Linux operating system, was tested specifically in the context of dynamic clamping, a demanding real-time task in which a computational system mimics the effects of nonlinear membrane conductances in living cells. The system is fast enough to represent dozens of nonlinear conductances in real time at clock rates well above 10 kHz. Conductances can be represented in deterministic form, or more accurately as discrete collections of stochastically gating ion channels. Tests were performed using a variety of complex models of nonlinear membrane mechanisms in excitable cells, including simulations of spatially extended excitable structures, and multiple interacting cells. Only in extreme cases does the computational load interfere with high-speed "hard" real-time processing (i.e., real-time processing that never falters). Freely available on the worldwide web, this experimental control system combines good performance. immense flexibility, low cost, and reasonable ease of use. It is easily adapted to any task involving real-time control, and excels in particular for applications requiring complex control algorithms that must operate at speeds over 1 kHz.

Computer Simulation↗
PubMed2003

Simultaneous modeling of abciximab plasma concentrations and ex vivo pharmacodynamics in patients undergoing coronary angioplasty.

An integrated structural pharmacokinetic/pharmacodynamic (PK/PD) model was developed for the glycoprotein IIb/IIIa antagonist abciximab administered to patients undergoing percutaneous transluminal coronary angioplasty. PK/PD data, in the form of plasma abciximab concentrations and ex vivo platelet aggregation in the presence of 20 microM adenosine diphosphate, were obtained from two previously conducted clinical studies. Study 1 consisted of patients who were given abciximab as a single intravenous injection of 0.25 mg/kg (n = 32). Patients in study 2 received an identical bolus dose, followed by a 36-h infusion at 0.125 microg/kg/min (n = 15). The PK component of the final model included drug-receptor binding, nonspecific distribution, and linear systemic clearance, whereas the PD module assumed that ex vivo dynamics were controlled by free plasma drug concentration. Mean PK/PD data from both studies were fitted simultaneously using nonlinear regression. PK profiles from both studies show rapidly decreasing plasma abciximab concentrations at early time points, but with extended terminal disposition phases. The maximum effect (Emax = 83.6%) was achieved rapidly and gradually returned to baseline values, although inhibition could be measured long after abciximab concentrations dropped below the detection limit. The final model well described the resulting PK/PD profiles and allowed for parameter estimation with relatively small coefficients of variation. Simulations were conducted to assess predicted receptor-occupancy and effects of selected parameters on PK/PD profiles. Models such as the one developed in this study demonstrate how drug binding to pharmacological targets may influence the PK of certain drugs and also provide a suitable paradigm for defining the PK/PD relationships of similar compounds.

Abciximab↗
PubMed2006

[Transient dynamics of excited states and nonlinear optical properties of InP nanoparticles].

The decay curves of the emission at different wavelength were measured. One nanosecond of transition lifetime of interband was obtained. The transient dynamics of InP nanoparticles was investigated by one color femtosecond pump-probe method at the wavelength of 800 nm. The experimental result shows that the saturation of exciton resonance results in photobleaching at 800 nm The decay process of the bleaching includes two components, i.e. the fast one from free carries scattering and the slow one from trapped carriers scattering. The nonlinear optical properties of InP nanoparticles were investigated by using femtosecond optical Kerr effect. The magnitude of chi3 for InP nanoparticles embedded in SiO2 sol-gel glass was calculated, and its origin was analyzed.

English Abstract↗
PubMed2003

Stationary transmission distribution of random spike trains by dynamical synapses.

Many nonlinearities in neural media are strongly dependent on spike timing jitter and intrinsic dynamics of synaptic transmission. Here we are interested in the stationary density of evoked postsynaptic potentials transmitted by depressing synapses for Poisson spike trains of fixed mean rates. We present a nonperturbative iterative method for computing the stationary density over increasing intervals. We conclude by showing how this method generalizes to other types of synapses, such as facilitating and hybrid synapses.

Journal Article↗
PubMed2005

Dynamical models of happiness.

A sequence of models for the time evolution of one's happiness in response to external events is described. These models with added nonlinearities can produce stable oscillations and chaos even without external events. Potential implications for psychotherapy and a personal approach to life are discussed.

Adaptation, Psychological↗
PubMed2004

Identification and control of a nonlinear discrete-time system based on its linearization: a unified framework.

This paper presents a unified theoretical framework for the identification and control of a nonlinear discrete-time dynamical system, in which the nonlinear system is represented explicitly as a sum of its linearized component and the residual nonlinear component referred to as a "higher order function." This representation substantially simplifies the procedure of applying the implicit function theorem to derive local properties of the nonlinear system, and reveals the role played by the linearized system in a more transparent form. Under the assumption that the linearized system is controllable and observable, it is shown that: 1) the nonlinear system is also controllable and observable in a local domain; 2) a feedback law exists to stabilize the nonlinear system locally; and 3) the nonlinear system can exactly track a constant or a periodic sequence locally, if its linearized system can do so. With some additional assumptions, the nonlinear system is shown to have a well-defined relative degree (delay) and zero-dynamics. If the zero-dynamics of the linearized system is asymptotically stable, so is that of the nonlinear one, and in such a case, a control law exists for the nonlinear system to asymptotically track an arbitrary reference signal exactly, in a neighborhood of the equilibrium state. The tracking can be achieved by using the state vector for feedback, or by using only the input and the output, in which case the nonlinear autoregressive moving-average (NARMA) model is established and utilized. These results are important for understanding the use of neural networks as identifiers and controllers for general nonlinear discrete-time dynamical systems.

Linear Models↗
PubMed2002

Population dynamics with a refuge: fractal basins and the suppression of chaos.

We consider the effect of coupling an otherwise chaotic population to a refuge. A rich set of dynamical phenomena is uncovered. We consider two forms of density dependence in the active population: logistic and exponential. In the former case, the basin of attraction for stable population growth becomes fractal, and the bifurcation diagrams for the active and refuge populations are chaotic over a wide range of parameter space. In the case of exponential density dependence, the dynamics are unconditionally stable (in that the population size is always positive and finite), and chaotic behavior is completely eradicated for modest amounts of dispersal. We argue that the use of exponential density dependence is more appropriate, theoretically as well as empirically, in a model of refuge dynamics.

Ecology↗
PubMed2004

On the mechanistic underpinning of discrete-time population models with complex dynamics.

We present a mechanistic underpinning for various discrete-time population models that can produce limit cycles and chaotic dynamics. Specific examples include the discrete-time logistic model and the Hassell model, which for a long time eluded convincing mechanistic interpretations, and also the Ricker- and Beverton-Holt models. We first formulate a continuous-time resource consumption model for the dynamics within a year, and from that we derive a discrete-time model for the between-year dynamics. Without influx of resources from the outside into the system, the resulting between-year dynamics is always overcompensating and hence may produce complex dynamics as well as extinction in finite time. We recover a connection between various standard types of continuous-time models for the resource dynamics within a year on the one hand and various standard types of discrete-time models for the population dynamics between years on the other. The model readily generalizes to several resource and consumer species as well as to more than two trophic levels for the within-year dynamics.

Animals↗
PubMed2003

Multiple attractors in stage-structured population models with birth pulses.

In most models of population dynamics, increases in population due to birth are assumed to be time-independent, but many species reproduce only during a single period of the year. A single species stage-structured model with density-dependent maturation rate and birth pulse is formulated. Using the discrete dynamical system determined by its Poincaré map, we report a detailed study of the various dynamics, including (a) existence and stability of nonnegative equilibria, (b) nonunique dynamics, meaning that several attractors coexist, (c) basins of attraction (defined as the set of the initial conditions leading to a certain type of attractor), (d) supertransients, and (e) chaotic attractors. The occurrence of these complex dynamic behaviour is related to the fact that minor changes in parameter or initial values can strikingly change the dynamic behaviours of system. Further, it is shown that periodic birth pulse, in effect, provides a natural period or cyclicity that allows multiple oscillatory solutions in the continuous dynamical systems.

Animals↗
PubMed2003

Characterizing direction of coupling from experimental observations.

We demonstrate that the direction of coupling of two interacting self-sustained electronic oscillators can be determined from the realizations of their signals. In our experiments, two electronic generators, operating in a periodic or a chaotic state, were subject to symmetrical or unidirectional coupling. In data processing, first the phases have been extracted from the observed signals and then the directionality of coupling was quantitatively estimated from the analysis of mutual dependence of the phase dynamics.

Models, Theoretical↗