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Results for “Nonlinear Dynamics”

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PubMed1982

Nonlinearity in pulmonary airway dynamics.

The paper describes an approach for determining nonlinearity in the pulmonary airway dynamic system, assuming a crude but linear model of the system. The linear electrical analogue representation of the dynamic system, found to be applicable only during the inspiratory phase of the respiration process, is considered as the basic model of the system. Control theory is used for nonlinearization of the dynamic process by considering the presence of an additional pressure source actuating the basic model and accounting for the system nonlinearity, which is found to be predominantly present during the expiratory phase. On analysis of the basic model, the form of the nonlinearizing signal is determined by examining the closeness between the model response and actual response of a typical patient. The use of this signal in a modified modelling of the process and in its computer simulation study is indicated.

Airway Resistance↗

PubMed1999

Dynamics underlying rhythmic and non-rhythmic variants of abnormal, waking delta activity.

OBJECT: We applied a new test, nonlinear cross prediction (NLCP), to investigate whether or polymorphic delta activity (PDA) and frontal intermittent rhythmic delta activity (FIRDA) reflect linear or nonlinear brain dynamics. Furthermore realistic models were constructed to explain the dynamical properties of PDA and FIRDA. METHODS: Forty-nine EEG time series with FIRDA and 40 time series with PDA were studied with the NLCP algorithm. This characterizes a time series in terms of its predictability, amplitude asymmetry, and time asymmetry, with the latter two measures reflecting nonlinearity. Parameters of an EEG model proposed by Lopes da Silva were adjusted to obtain time series resembling PDA and FIRDA. RESULTS: FIRDA was more predictable than PDA. Most PDA segments could not be distinguished from linearly filtered noise. In contrast, FIRDA activity showed strong evidence of nonlinear dynamics. These dynamical properties of PDA and FIRDA could be reproduced by the Lopes da Silva model. PDA and FIRDA reflect a point attractor and a limit cycle attractor, respectively, perturbed by dynamical noise. CONCLUSION: Experimental analysis and modeling of the data suggest that PDA and FIRDA reflect fundamentally different types of brain dynamics. While PDA is filtered noise, reflecting low-level, random input to cortical networks, FIRDA may reflect limit-cycle oscillations due to increased excitation.

Adult↗

PubMed2001

Nonlinear turbulent magnetic diffusion and mean-field dynamo.

The nonlinear coefficients defining the mean electromotive force (i.e., the nonlinear turbulent magnetic diffusion, the nonlinear effective velocity, the nonlinear kappa tensor, etc.) are calculated for an anisotropic turbulence. A particular case of an anisotropic background turbulence (i.e., the turbulence with zero-mean magnetic field) with one preferential direction is considered. It is shown that the toroidal and poloidal magnetic fields have different nonlinear turbulent magnetic diffusion coefficients. It is demonstrated that even for a homogeneous turbulence there is a nonlinear effective velocity that exhibits diamagnetic or paramagnetic properties depending on the anisotropy of turbulence and the level of magnetic fluctuations in the background turbulence. The diamagnetic velocity results in the field being pushed out from the regions with stronger mean magnetic field, while the paramagnetic velocity causes the magnetic field to be concentrated in the regions with stronger field. Analysis shows that an anisotropy of turbulence strongly affects the nonlinear turbulent magnetic diffusion, the nonlinear effective velocity, and the nonlinear alpha effect. Two types of nonlinearities (algebraic and dynamic) are also discussed. The algebraic nonlinearity implies a nonlinear dependence of the mean electromotive force on the mean magnetic field. The dynamic nonlinearity is determined by a differential equation for the magnetic part of the alpha effect. It is shown that for the alphaOmega axisymmetric dynamo the algebraic nonlinearity alone (which includes the nonlinear alpha effect, the nonlinear turbulent magnetic diffusion, the nonlinear effective velocity, etc.) cannot saturate the dynamo generated mean magnetic field while the combined effect of the algebraic and dynamic nonlinearities limits the mean magnetic field growth.

Journal Article↗

PubMed2004

Nonlinear modeling of the dynamic effects of arterial pressure and CO2 variations on cerebral blood flow in healthy humans.

The effect of spontaneous beat-to-beat mean arterial blood pressure fluctuations and breath-to-breath end-tidal CO2 fluctuations on beat-to-beat cerebral blood flow velocity variations is studied using the Laguerre-Volterra network methodology for multiple-input nonlinear systems. The observations made from experimental measurements from ten healthy human subjects reveal that, whereas pressure fluctuations explain most of the high-frequency blood flow velocity variations (above 0.04 Hz), end-tidal CO2 fluctuations as well as nonlinear interactions between pressure and CO2 have a considerable effect in the lower frequencies (below 0.04 Hz). They also indicate that cerebral autoregulation is strongly nonlinear and dynamic (frequency-dependent). Nonlinearities are mainly active in the low-frequency range (below 0.04 Hz) and are more prominent in the dynamics of the end-tidal CO2-blood flow velocity relationship. Significant nonstationarities are also revealed by the obtained models, with greater variability evident for the effects of CO2 on blood flow velocity dynamics.

Adult↗

PubMed2004

On time-space of nonlinear phenomena with Gompertzian dynamics.

This paper describes a universal relationship between time and space for a nonlinear process with Gompertzian dynamics, such as growth. Gompertzian dynamics implicates a coupling between time and space. Those two categories are related to each other through a linear function of their logarithms. Moreover, we demonstrate that the spatial fractal dimension is a function of both scalar time and the temporal fractal dimension. The Gompertz function reflects the equilibrium of regular states, that is, states with dynamics that are predictable for any time-point (e.g., sinusoidal glycolytic oscillations) and chaotic states, that is, states with dynamics that are unpredictable in time, but are characterized by certain regularities (e.g., the existence of strange attractor for any biochemical reaction). We conclude that both this equilibrium and volume of the available complementary Euclidean space determine temporal and spatial expansion of a process with Gompertzian dynamics.

Animals↗

PubMed2005

Arbitrary nonlinearities in convective population dynamics with small diffusion.

Convective counterparts of variants of the nonlinear Fisher equation which describes reaction diffusion systems in population dynamics are studied with the help of an analytic prescription and shown to lead to interesting consequences for the evolution of population densities. The initial-value problem is solved explicitly for some cases, and for others it is shown how to find traveling-wave solutions analytically. The effect of adding diffusion to the convective equations is first studied through exact analysis through a piecewise linear representation of the nonlinearity. Using an appropriate small parameter suggested by that analysis, a perturbative treatment is developed to treat the case in which the convective evolution is augmented by a small amount of diffusion.

Animals↗

PubMed2002

Nonlinear analysis of dynamic binding in affinity capillary electrophoresis demonstrated for inclusion complexes of beta-cyclodextrin.

The stability of the molecular host-guest inclusion complexes of beta-cyclodextrin with benzoate and four different hydroxybenzoates is investigated. For the measurement of the binding constants an experimental method is devised that is based on affinity capillary electrophoresis (ACE) with indirect UV absorbance detection. We derive an explicit equation for effective mobilities in ACE experiments without violation of rigorous mass balance. This equation is employed in the nonlinear least-squares analyses of the experimental data yielding binding constants of 48+/-2 M(-1) for benzoate, 299+/-38 M(-1) for 2-hydroxybenzoate, 37+/-1 M(-1) for 3-hydroxybenzoate, 228+/-9 M(-1) for 4-hydroxybenzoate, and 895+/-110 M(-1) in the case of 2,4-dihydroxybenzoate.

Cyclodextrins↗

PubMed1995

Finite element analysis of nonlinear pulsatile suspension flow dynamics in blood vessels with aneurysm.

A nonlinear pulsatile suspension flow in a dilated vessel is numerically analysed. Two sets of highly coupled nonlinear partial differential equations governing the suspension flow are numerically solved, to simulate the suspension flow dynamics. A transient velocity-pressure (UVP) finite element method (FEM) and a stable time integration scheme, based on a predictor-corrector strategy, with constant error monitoring are employed in the flow analysis. The pulsatile suspension flow is characterized by analysing the flow, pressure and stress fields. Effects of the nonlinear particulate phase on the nonlinear suspending fluid phase are brought out by comparing the suspension flow results with those of homogeneous flow. Particles are seen to dampen the flow velocity, wall and central axis pressure, pressure gradient and wall shear stress. time-dependent recirculation regions which are sensitive to the presence of particles are seen in the dilated portion of the vessel. These recirculation regions favour thrombogenesis. The nonlinear effects due to the vessel geometry and those due to the convective terms dominate the dampening effect of the particles. These nonlinear effects are depicted through the transverse velocity and pressure plots. Wall shear stresses of suspension flow are not only high but also alternate in direction.

Algorithms↗

PubMed1999

Dynamics of a nonlinear parametrically excited partial differential equation.

We investigate a parametrically excited nonlinear Mathieu equation with damping and limited spatial dependence, using both perturbation theory and numerical integration. The perturbation results predict that, for parameters which lie near the 2:1 resonance tongue of instability corresponding to a single mode of shape cos nx, the resonant mode achieves a stable periodic motion, while all the other modes are predicted to decay to zero. By numerically integrating the p.d.e. as well as a 3-mode o.d.e. truncation, the predictions of perturbation theory are shown to represent an oversimplified picture of the dynamics. In particular it is shown that steady states exist which involve many modes. The dependence of steady state behavior on parameter values and initial conditions is investigated numerically. (c) 1999 American Institute of Physics.

Journal Article↗

PubMed1955