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At least 1,081 records · Page 60Linked to original sources
PubMed2000

Quantification of depth of anesthesia by nonlinear time series analysis of brain electrical activity

We investigate several quantifiers of the electroencephalogram (EEG) signal with respect to their ability to indicate depth of anesthesia. For 17 patients anesthetized with sevoflurane, three established measures (two spectral and one based on the bispectrum), as well as a phase space based nonlinear correlation index were computed from consecutive EEG epochs. In the absence of an independent way to determine anesthesia depth, the standard was derived from measured blood plasma concentrations of the anesthetic via a pharmacokinetic/pharmacodynamic model for the estimated effective brain concentration of sevoflurane. In most patients, the highest correlation is observed for the nonlinear correlation index D*. In contrast to spectral measures, D* is found to decrease monotonically with increasing (estimated) depth of anesthesia, even when a "burst-suppression" pattern occurs in the EEG. The findings show the potential for applications of concepts derived from the theory of nonlinear dynamics, even if little can be assumed about the process under investigation.

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PubMed2000

Symbolic sequence statistical analysis for free liquid jets

Free liquid jets are investigated here as nonlinear dynamical systems. A scalar time series corresponding to the time evolution of the jet diameter is then used to investigate the underlying dynamics in terms of reconstructed phase portraits, Poincare sections, and first-return maps. Particular attention is paid to characterizing the behavior using symbolic sequence statistics that enable different atomization regimes to be distinguished. Such statistics are first applied on theoretical maps to support the results obtained on the jet dynamics.

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PubMed2001

Periodic orbits and topological entropy of delayed maps.

The periodic orbits of a nonlinear dynamical system provide valuable insight into the topological and metric properties of its chaotic attractors. In this paper we describe general properties of periodic orbits of dynamical systems with feedback delay. In the case of delayed maps, these properties enable us to provide general arguments about the boundedness of the topological entropy in the high delay limit. As a consequence, all the metric entropies can be shown to be bounded in this limit. The general considerations are illustrated in the cases of Bernoulli-like and Hénon-like delayed maps.

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PubMed2001

Diffusion by extrinsic noise in the kicked Harper map.

A significantly improved analytic understanding of the extrinsically driven diffusion process is presented in a nonlinear dynamical system in which the phase space is divided into periodic two-dimensional tiles of regular motion, separated by a connected separatrix network (web) [previously studied by A. J. Lichtenberg and Blake P. Wood, Phys. Rev. Lett. 62, 2213 (1989)]. The system is represented by the usual "kicked Harper map" with added extrinsic noise terms. Three different diffusion regimes are found depending upon the strength of the extrinsic perturbation l relative to the web and regular motions. When the extrinsic noise is dominant over the intrinsic stochasticity and the regular rotation motions in the tile, diffusion obeys the random phase scaling l(2). When the extrinsic noise is dominant over the intrinsic stochasticity, but weaker than the regular rotation motion, the diffusion scales as lK(1/2), where K is the strength of the intrinsic kick. These findings agree well with numerical simulation results. When the extrinsic noise process is weaker than the stochastic web process, we analytically reproduce the well-known numerical result: The web diffusion is reduced by the ratio of phase-space areas of intrinsic to extrinsic stochasticity.

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PubMed2001

Detection of hidden regimes in stochastic cyclostationary time series.

Stationary stochastic time series with nonlinear dynamics can feature a probability density function (PDF) with distinct local maxima associated with distinct regimes. For nonstationary time series, on the other hand, such regimes are not necessarily reflected in the shape of the PDF. This occurs when the duration of a regime is too short for the PDF to adjust, and such a regime is called a "hidden" regime. This paper presents an algorithm that allows one to detect hidden regimes in cyclostationary stochastic Markovian time series. The method involves analysis of an appropriately windowed time series, from which the drift and diffusion coefficients of the associated Fokker-Planck equation are estimated. The success of the algorithm is illustrated using synthetic time series with both additive and multiplicative noise.

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PubMed2001

Local and global control of high-period unstable orbits in reversible maps.

We study the nonlinear dynamics of a complex system, described by a two-dimensional reversible map. The phase space of this map exhibits elements typical of Hamiltonian systems (stability islands) as well as of dissipative systems (attractor). Due to the interaction between the stability islands and the attractor, the transition to chaos in this system occurs through the collapse of the stability island and stochastization of the limiting-cycles orbits. We show how to apply the method of discrete parametric control to stabilize unstable high-period orbits. To achieve highly efficient control we introduce the concepts of local and global control. These concepts are useful in situations where there are "dangerous" points on the target orbit, i.e., the points where the probability of breakdown of control is high. As a result, the dangerous points turn out to be much more sensitive to external noise than other points on the orbit, and only the dangerous points determine how effective the control is.

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PubMed2001

Embedding of multidimensional time-dependent observations.

A method is proposed to reconstruct dynamic attractors by embedding of multivariate observations of dynamic nonlinear processes. The Takens embedding theory is combined with independent component analysis to transform the embedding into a vector space of linearly independent vectors (phase variables). The method is successfully tested against prediction of the unembedded state vector in two case studies of simulated chaotic processes.

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PubMed2001

Nonhyperbolic escape and changes in phase-space stability structures in laser-induced multiphoton dissociation of a diatomic molecule.

The dependence of photodissociation of a diatomic molecule (vibrating according to the Morse potential) on the frequency of the laser field that induces it, is studied in the context of classical nonlinear dynamics. First, it is observed that as the laser frequency increases towards the harmonic frequency of the potential, a transition from stabilization due to Kolmogorov-Arnold-Moser tori to stabilization caused by the resonance stability island occurs. Then, considering the photodissociation as a nonhyperbolic half-scattering process, we investigate the influence of these changes in the phase space stability structures on dissociation dynamics via the examination of the fractal set of singularities appearing in the time-delay function of the initial state. It is found that the effective fractal dimension of this set (a finite-scale approximation of the exact dimension which is always equal to 1) and the percentage of its singularities provide a link between these changes and the dissociation rate.

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PubMed2001

Solitons on a zigzag-runged ladder lattice.

The nonlinear dynamical model on a two-leg ladder lattice with the rungs arranged into a zigzag chain is proposed. The lattice contains two structure elements (molecules) in the unit cell. As a result, the system exhibits the two-branch spectrum in its low-amplitude limit. The similar two branches are shown to be observed in high-amplitude soliton solutions too. The integrability of the model is proved and the one-soliton solutions are explicitly presented and analyzed. The model Hamiltonian, as well as the basic conserved quantities are found.

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PubMed2002

Analytical characterization of spontaneous firing in networks of developing rat cultured cortical neurons.

We have used a multiunit electrode array in extracellular recording to investigate changes in the firing patterns in networks of developing rat cortical neurons. The spontaneous activity of continual asynchronous firing or the alternation of asynchronous spikes and synchronous bursts changed over time so that activity in the later stages consisted exclusively of synchronized bursts. The spontaneous coordinated activity in bursts produced a variability in interburst interval (IBI) sequences that is referred to as "form." The stochastic and nonlinear dynamical analysis of IBI sequences revealed that these sequences reflected a largely random process and that the form for relatively immature neurons was largely oscillatory while the form for the more mature neurons was Poisson-like. The observed IBI sequences thus showed changes in form associated with both the intrinsic properties of the developing cells and the neural response to correlated synaptic inputs due to interaction between the developing neural circuits.

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PubMed2002

Self-similar solutions for conic cusps formation at the surface of dielectric liquids in electric field.

The nonlinear dynamics is studied for the free surface of an ideal dielectric fluid in an electric field. Self-similar solutions of electrohydrodynamic equations describing the formation of surface conic cusps are revealed. The behavior of physical quantities (field strength, fluid velocity, and surface curvature) near the singularity is established. The threshold value of the fluid dielectric constant required for the proposed mechanism of a cusp development is found.

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PubMed2002

Stress fluctuations in sheared Stokesian suspensions.

We report an analysis, using the tools of nonlinear dynamics and chaos theory, of the fluctuations in the stress determined from simulations of shear flow of Stokesian suspensions. The simulations are for shear between plane parallel walls of a suspension of rigid identical spheres in a Newtonian fluid, over a range of particle concentration. By analyzing the time series of the stress, we find that the dynamics underlying these fluctuations is deterministic, low-dimensional, and chaotic. We use the dynamic and metric invariants of the underlying dynamics as a means of characterizing suspension behavior. The dimension of the chaotic attractor increases with particle concentration, indicating the increasing influence of multiple-body interactions on the rheology of the suspension with rise in particle concentration. We use our analysis to make accurate predictions of the short-term evolution of a stress component from its preceding time series, and predict the evolution of one component of the stress using the time series of another. We comment on the physical origin of the chaotic stress fluctuations, and on the implications of our results on the relation between the microstructure and the stress.

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PubMed2003

Relationship between the nonlinear ferroelectric and liquid crystal models for microtubules.

Microtubules (MTs), which are the main components of the cytoskeleton, are important in a variety of cellular activities, but some physical properties underlying the most important features of their behavior are still lacking satisfactory explanation. One of the essential enigmas regarding the energy balance in MTs is the hydrolysis of the exchangeable guanosine 5'-triphosphate bound to the beta monomer of the molecule. The energy released in the hydrolysis process amounts to 6.25 x 10(-20) J and has been the subject of many attempts to answer the questions of its utilization. Earlier, we put forward a hypothesis that this energy can cause a local conformational distortion of the dimer. This distortion should have nonlinear character and could lead to the formation of a traveling kink soliton. In this paper we use the formalism of the liquid crystal theory to consider the nonlinear dynamics of MTs. We demonstrate that this new model is formally equivalent to our earlier ferroelectric model which was widely exploited in an attempt to elucidate some important dynamical activities in MTs. We also study the stability of kink solitons against small perturbations and their unusual mutual interactions as well as the interactions with structural inhomogeneities of MTs. Our new approach based on liquid crystal properties of microtubules has been recently corroborated by new insights gained from the electrostatic properties of tubulin and microtubules.

Animals↗
PubMed2003

Quantum morphogenesis: a variation on Thom's catastrophe theory.

Noncommutative propositions are characteristic of both quantum and nonquantum (sociological, biological, and psychological) situations. In a Hilbert space model, states, understood as correlations between all the possible propositions, are represented by density matrices. If systems in question interact via feedback with environment, their dynamics is nonlinear. Nonlinear evolutions of density matrices lead to the phenomenon of morphogenesis that may occur in noncommutative systems. Several explicit exactly solvable models are presented, including "birth and death of an organism" and "development of complementary properties."

Animals↗
PubMed2003

Small aspect ratio Taylor-Couette flow: onset of a very-low-frequency three-torus state.

The nonlinear dynamics of Taylor-Couette flow in a small aspect ratio annulus (where the length of the cylinders is half of the annular gap between them) is investigated by numerically solving the full three-dimensional Navier-Stokes equations. The system is invariant to arbitrary rotations about the annulus axis and to a reflection about the annulus half-height, so that the symmetry group is SO(2)xZ2. In this paper, we systematically investigate primary and subsequent bifurcations of the basic state, concentrating on a parameter regime where the basic state becomes unstable via Hopf bifurcations. We derive the four distinct cases for the symmetries of the bifurcated orbit, and numerically find two of these. In the parameter regime considered, we also locate the codimension-two double Hopf bifurcation where these two Hopf bifurcations coincide. Secondary Hopf bifurcations (Neimark-Sacker bifurcations), leading to modulated rotating waves, are subsequently found and a saddle-node-infinite-period bifurcation between a stable (node) and an unstable (saddle) modulated rotating wave is located, which gives rise to a very-low-frequency three-torus. This paper provides the computed example of such a state, along with a comprehensive bifurcation sequence leading to its onset.

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PubMed2003

Explicit symplectic integrator for s-dependent static magnetic field.

This paper reports our recent work on explicit symplectic integration techniques for the charged particle motion in an s-dependent static magnetic field. Using the extended phase space, symplectic integrators can be developed for Hamiltonians with or without the paraxial approximation using either the space or time as an independent variable. This work extends the successful element-by-element tracking method for studying single-particle nonlinear dynamics to a set of s-dependent magnetic elements. Important applications of this work include the studies of the charged particle dynamics in a storage ring with various insertion devices, superconducting magnets, large aperture magnets with significant fringe fields, and solenoid magnets in the interaction region. Consequently, this work is expected to make an impact on design and optimal operation of existing and future light source rings and high energy physics accelerators.

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PubMed2003

Density fingering of an exothermic autocatalytic reaction.

Density fingering of exothermic autocatalytic fronts in vertically oriented porous media and Hele-Shaw cells is studied theoretically for chemical reactions where the solutal and thermal contribution to density changes have opposite signs. The competition between these two effects leads to thermal plumes for ascending fronts. The descending fronts behave strikingly differently as they can feature, for some values of the parameters, fingers of constant amplitude and wavelength. The differences between up and down going fronts are discussed in terms of dispersion curves and nonlinear dynamics. The theoretically predicted dispersion curves are experimentally evidenced with the chlorite-tetrathionate reaction.

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