SEARCH · PubMed Health

Results for “Nonlinear Dynamics”

Explore indexed PubMed citations for clinical trials, systematic reviews and public health research. Read source abstracts and follow each citation to its original PubMed record.

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

At least 1,099 records · Page 61Linked to original sources

PubMed2004

Anomalous diffusion and collapse of self-gravitating Langevin particles in D dimensions.

We address the generalized thermodynamics and the collapse of a system of self-gravitating Langevin particles exhibiting anomalous diffusion in a space of dimension D. This is a basic model of stochastic particles in interaction. The equilibrium states correspond to polytropic configurations similar to stellar polytropes and polytropic stars. The index n of the polytrope is related to the exponent of anomalous diffusion. We consider a high-friction limit and reduce the problem to the study of the nonlinear Smoluchowacute;ski-Poisson system. We show that the associated Lyapunov functional is the Tsallis free energy. We discuss in detail the equilibrium phase diagram of self-gravitating polytropes as a function of D and n, and determine their stability by using turning point arguments and analytical methods. When no equilibrium state exists, we investigate self-similar solutions of the nonlinear Smoluchowski-Poisson system describing the collapse. Our stability analysis of polytropic spheres can be used to settle the generalized thermodynamical stability of self-gravitating Langevin particles as well as the nonlinear dynamical stability of stellar polytropes, polytropic stars and polytropic vortices. Our study also has applications concerning the chemotactic aggregation of bacterial populations.

Journal Article↗

PubMed2004

Universal instabilities of radio-frequency traps.

Using standard tools of nonlinear dynamics we analyze recently discovered instabilities of radio-frequency charged-particle traps. In the cw-driven cylindrical Kingdon trap the instabilities occur at the two values eta*(3) =3.6130467...and eta*(4) =4.4311244...of the trap's control parameter eta. Analytical estimates based on the theory of Mathieu functions predict eta*(3) =pi square root of [(363-32 pi(2))/(66 pi square root of (6-48 pi(2))]=3.6923922...and eta*(4) = [(square root of pi)/2) x [(363-32 pi(2))/(square root of (1089+48 pi(2))-12 pi)](1/2) =4.4965466... The kicked Kingdon trap, an analytically solvable model, predicts eta*(3) = 1/3 square root of 105=3.4156502...and eta*(4) = square root of 17=4.1231056... We show that similar instabilities occur in the two-particle Paul trap and the cw-driven spherical Kingdon trap.

Journal Article↗

PubMed2004

Energy localization in the Peyrard-Bishop DNA model.

We study energy localization on the oscillator chain proposed by Peyrard and Bishop to model DNA. We search numerically for conditions with initial energy in a small subgroup of consecutive oscillators of a finite chain and such that the oscillation amplitude is small outside this subgroup on a long time scale. We use a localization criterion based on the information entropy and verify numerically that such localized excitations exist when the nonlinear dynamics of the subgroup oscillates with a frequency inside the reactive band of the linear chain. We predict a mimium value for the Morse parameter (micro>2.25) (the only parameter of our normalized model), in agreement with the numerical calculations (an estimate for the biological value is micro=6.3 ). For supercritical masses, we use canonical perturbation theory to expand the frequencies of the subgroup and we calculate an energy threshold in agreement with the numerical calculations.

Biophysics↗

PubMed2004

Observation of robust quantum resonance peaks in an atom optics kicked rotor with amplitude noise.

The effect of pulse train noise on the quantum resonance peaks of the atom optics kicked rotor is investigated experimentally. Quantum resonance peaks in the late time mean energy of the atoms are found to be surprisingly robust against all levels of noise applied to the kicking amplitude, while even small levels of noise on the kicking period lead to their destruction. The robustness to amplitude noise of the resonance peak and of the fall-off in mean energy to either side of this peak are explained in terms of the occurrence of stable, epsilon classical dynamics [Nonlinearity 16, 1381 (2003)]] around each quantum resonance.

Journal Article↗

PubMed2005

Cluster-weighted modeling: estimation of the Lyapunov spectrum in driven systems.

Cluster-weighted modeling based techniques are shown to be accurate, efficient, and robust in application to the problem of computing the Lyapunov spectrum from time-series data. We develop a method that is appropriate for application to driven nonlinear dynamical systems and show, in particular, that it is possible to estimate both global and local Lyapunov exponents through this technique. For dynamics on strange nonchaotic attractors, the present approach correctly determines a largest Lyapunov exponent that is negative.

Journal Article↗

PubMed2005

Thermodynamics of magnetohydrodynamic flows with axial symmetry.

We present strategies based upon optimization principles in the case of the axisymmetric equations of magnetohydrodynamics (MHD). We derive the equilibrium state by using a minimum energy principle under the constraints of the MHD axisymmetric equations. We also propose a numerical algorithm based on a maximum energy dissipation principle to compute in a consistent way the nonlinearly dynamically stable equilibrium states. Then, we develop the statistical mechanics of such flows and recover the same equilibrium states giving a justification of the minimum energy principle. We find that fluctuations obey a Gaussian shape and we make the link between the conservation of the Casimirs on the coarse-grained scale and the process of energy dissipation. We contrast these results with those of two-dimensional hydrodynamical turbulence where the equilibrium state maximizes a H function at fixed energy and circulation and where the fluctuations are nonuniversal.

Journal Article↗

PubMed2005

Multimode lasing in two-dimensional fully chaotic cavity lasers.

Multimode lasing in a fully chaotic cavity is investigated numerically by using a nonlinear dynamics model. We report a transition process from single-mode lasing to multimode lasing and reveal interactions among the lasing modes. In particular, both mode-pulling and mode-pushing interactions are shown to decrease the number of effective lasing modes. In addition, coexistence of different types of attractors of the final lasing states is numerically confirmed.

Journal Article↗

PubMed2005

Recurrence time analysis, long-term correlations, and extreme events.

The recurrence times between extreme events have been the central point of statistical analyses in many different areas of science. Simultaneously, the Poincaré recurrence time has been extensively used to characterize nonlinear dynamical systems. We compare the main properties of these statistical methods pointing out their consequences for the recurrence analysis performed in time series. In particular, we analyze the dependence of the mean recurrence time and of the recurrence time statistics on the probability density function, on the interval whereto the recurrences are observed, and on the temporal correlations of time series. In the case of long-term correlations, we verify the validity of the stretched exponential distribution, which is uniquely defined by the exponent gamma, at the same time showing that it is restricted to the class of linear long-term correlated processes. Simple transformations are able to modify the correlations of time series leading to stretched exponentials recurrence time statistics with different gamma, which shows a lack of invariance under the change of observables.

Journal Article↗

PubMed2005

Excitation functions of coupling.

The responses of nonlinear dynamics of two classes to coupling are investigated. It is shown both analytically and numerically that coupling has an excitation ability in a network of the linearly coupled systems. That is, when an uncoupled system is degenerated to a stable steady state from a limit cycle but in the "marginal" state due to the system parameter, an appropriate coupling strength can excite the limit cycle such that the coupled systems exhibit synchronous oscillation; when the uncoupled system is in a stable limit cycle but close to a chaotic attractor, a certain coupling strength can induce the chaotic attractor such that the coupled systems reach chaotic synchronization. Such excitation functions of coupling are different from its traditional role where coupling mainly synchronizes the coupled systems with the original dynamics of the uncoupled system.

Journal Article↗

PubMed2005

Intrinsic coherence resonance in an electrochemical cell.

We study the interaction of intrinsic electrochemical noise with autonomous nonlinear dynamics of a three-electrode electrochemical cell. The amplitude of this intrinsic (internal) noise, regulated by the concentration of chloride ions, is monotonically increased and the provoked dynamics is analyzed. The experimentally constructed coherence factor beta versus the concentration of the chloride ions' curve has a unimodal shape indicating the emergence of intrinsic coherence resonance. The abscissa for the maxima of this unimodal curve corresponds to the optimum value of intrinsic noise where maximum regularity of the invoked dynamics is observed.

Journal Article↗

PubMed2005

Approach to predictability via anticipated synchronization.

Predictability of chaotic systems is limited, in addition to the precision of the knowledge of the initial conditions, by the error of the models used to extract the nonlinear dynamics from the time series. In this paper, we analyze the predictions obtained from the anticipated synchronization scheme using a chain of slave neural network approximate replicas of the master system. We compare the maximum prediction horizons obtained with those attainable using standard prediction techniques.

Journal Article↗

PubMed2006

Response of discrete nonlinear systems with many degrees of freedom.

We study the response of a large array of coupled nonlinear oscillators to parametric excitation, motivated by the growing interest in the nonlinear dynamics of microelectromechanical and nanoelectromechanical systems (MEMS and NEMS). Using a multiscale analysis, we derive an amplitude equation that captures the slow dynamics of the coupled oscillators just above the onset of parametric oscillations. The amplitude equation that we derive here from first principles exhibits a wave-number dependent bifurcation similar in character to the behavior known to exist in fluids undergoing the Faraday wave instability. We confirm this behavior numerically and make suggestions for testing it experimentally with MEMS and NEMS resonators.

Journal Article↗

PubMed2006

Synchronization properties of two self-oscillating semiconductor lasers subject to delayed optoelectronic mutual coupling.

We theoretically investigate the nonlinear dynamics and synchronization properties between two mutually coupled semiconductor lasers units. Each unit can self-oscillate by means of delayed optoelectronic feedback loops. The mutual optoelectronic interactions between the laser units take into account the finite propagation time of the signals. Under perfectly symmetric conditions, we find different "death by delay" islands that persist for instantaneous coupling. The appearance of (zero lag) isochronous chaotic synchronization, under appropriate driving conditions, is another distinctive feature of the delayed feedback loops in the laser units. For slightly asymmetric operation, we obtain frequency locked bands (Arnold Tongue) whose width periodically changes with the coupling delay time.

Journal Article↗

PubMed2000

Statistical mechanics of a discrete nonlinear system

Statistical mechanics of the discrete nonlinear Schrodinger equation is studied by means of analytical and numerical techniques. The lower bound of the Hamiltonian permits the construction of standard Gibbsian equilibrium measures for positive temperatures. Beyond the line of T = infinity, we identify a phase transition through a discontinuity in the partition function. The phase transition is demonstrated to manifest itself in the creation of breatherlike localized excitations. Interrelation between the statistical mechanics and the nonlinear dynamics of the system is explored numerically in both regimes.

Journal Article↗

PubMed2001

Stable quantum computation of unstable classical chaos.

We show on the example of the Arnold cat map that classical chaotic systems can be simulated with exponential efficiency on a quantum computer. Although classical computer errors grow exponentially with time, the quantum algorithm with moderate imperfections is able to simulate accurately the unstable chaotic classical nonlinear dynamics for long times. The algorithm can be easily implemented on systems of a few qubits.

Journal Article↗

PubMed2001

Nonstationary time-series analysis: accurate reconstruction of driving forces.

We propose a simple method for the accurate reconstruction of slowly changing external forces acting on nonlinear dynamical systems. The method traces the evolution of the external force by locally linearizing the map dependency with the shifting parameter. Application of our algorithm to synthetic data corresponding to discrete models of evolving ecosystems shows an accuracy that outperforms those of previous methods in the literature. In addition, an application to the real-world sunspot time series recovers recently reported changes in solar activity during the last century.

Journal Article↗

PubMed2002

Avalanche excitations of fast particles in quasi-2D cold dusty-plasma liquids.

We study the spatiotemporal cooperative microexcitations in quasi-2D cold dusty-plasma liquids from the view of the coupled subexcitable nonlinear dynamical system. Under the interplay of thermal noise and mutual coupling, cooperative fast-particle clusters are excited in the xyt space. The fast hopping plays a major role in the superdiffusion with non-Gaussian velocity distribution and causes the loss of bond-orientation memory. The size distribution of the excited clusters in the xyt space follows a similar avalanche-type power-law relation as in other subexcitable systems.

Journal Article↗

PubMed2002

Conduction block in one-dimensional heart fibers.

We present a nonlinear dynamical systems analysis of the transition to conduction block in one-dimensional cardiac fibers. We study a simple model of wave propagation in heart tissue that depends only on the recovery of action potential duration and conduction velocity. If the recovery function has slope >or=1 and the velocity recovery function is nonconstant, rapid activation causes dynamical heterogeneity and finally conduction block away from the activation site. This dynamical mechanism may play a role in the initiation and breakup of spiral waves in excitable media.

Action Potentials↗