Biomedical subjects

Ira B Schwartz

Publications and source records attributed to Ira B Schwartz.

15 recordsLinked to original sources

PubMed2006

Predictions of ultraharmonic oscillations in coupled arrays of limit cycle oscillators.

Coupled distinct arrays of nonlinear oscillators have been shown to have a regime of high frequency, or ultraharmonic, oscillations that are at multiples of the natural frequency of individual oscillators. The coupled array architectures generate an in-phase high-frequency state by coupling with an array in an antiphase state. The underlying mechanism for the creation and stability of the ultraharmonic oscillations is analyzed. A class of interarray coupling is shown to create a stable, in-phase oscillation having frequency that increases linearly with the number of oscillators, but with an amplitude that stays fairly constant. The analysis of the theory is illustrated by numerical simulation of coupled arrays of Stuart-Landau limit cycle oscillators.

Journal Article↗

PubMed2006

Synchronization and time shifts of dynamical patterns for mutually delay-coupled fiber ring lasers.

A pair of coupled erbium doped fiber ring lasers is used to explore the dynamics of coupled spatiotemporal systems. The lasers are mutually coupled with a coupling delay less than the cavity round-trip time. We study synchronization between the two lasers in the experiment and in a delay differential equation model of the system. Because the lasers are internally perturbed by spontaneous emission, we include a noise source in the model to obtain stochastic realizations of the deterministic equations. Both amplitude synchronization and phase synchronization are considered. We use the Hilbert transform to define the phase variable and compute phase synchronization. We find that synchronization increases with coupling strength in the experiment and the model. When the time series from two lasers are time shifted in either direction by the delay time, approximately equal synchronization is frequently observed, so that a clear leader and follower cannot be identified. We define an algorithm to determine which laser leads the other when the synchronization is sufficiently different with one direction of time shift, and statistics of switches in leader and follower are studied. The frequency of switching between leader and follower increases with coupling strength, as might be expected since the lasers mutually influence each other more effectively with stronger coupling.

Computer Simulation↗

PubMed2005

Chaotic desynchronization of multistrain diseases.

Multistrain diseases are diseases that consist of several strains, or serotypes. The serotypes may interact by antibody-dependent enhancement (ADE), in which infection with a single serotype is asymptomatic, but infection with a second serotype leads to serious illness accompanied by greater infectivity. It has been observed from serotype data of dengue hemorrhagic fever that outbreaks of the four serotypes occur asynchronously. Both autonomous and seasonally driven outbreaks were studied in a model containing ADE. For sufficiently small ADE, the number of infectives of each serotype synchronizes, with outbreaks occurring in phase. When the ADE increases past a threshold, the system becomes chaotic, and infectives of each serotype desynchronize. However, certain groupings of the primary and secondary infectives remain synchronized even in the chaotic regime.

Animals↗

PubMed2005

Dynamic effects of antibody-dependent enhancement on the fitness of viruses.

Antibody-dependent enhancement (ADE), a phenomenon in which viral replication is increased rather than decreased by immune sera, has been observed in vitro for a large number of viruses of public health importance, including flaviviruses, coronaviruses, and retroviruses. The most striking in vivo example of ADE in humans is dengue hemorrhagic fever, a disease in which ADE is thought to increase the severity of clinical manifestations of dengue virus infection by increasing virus replication. We examine the epidemiological impact of ADE on the prevalence and persistence of viral serotypes. Using a dynamical system model of n cocirculating dengue serotypes, we find that ADE may provide a competitive advantage to those serotypes that undergo enhancement compared with those that do not, and that this advantage increases with increasing numbers of cocirculating serotypes. Paradoxically, there are limits to the selective advantage provided by increasing levels of ADE, because greater levels of enhancement induce large amplitude oscillations in incidence of all dengue virus infections, threatening the persistence of both the enhanced and nonenhanced serotypes. Although the models presented here are specifically designed for dengue, our results are applicable to any epidemiological system in which partial immunity increases pathogen replication rates. Our results suggest that enhancement is most advantageous in settings where multiple serotypes circulate and where a large host population is available to support pathogen persistence during the deep troughs of ADE-induced large amplitude oscillations of virus replication.

Animals↗

PubMed2005

Scaling behavior of laser population dynamics with time-delayed coupling: theory and experiment.

We study the influence of asymmetric coupling strengths on the onset of light intensity oscillations in an experimental system consisting of two semiconductor lasers cross coupled optoelectronically with a time delay. We discover a scaling law that relates the amplitudes of oscillations and the coupling strengths. These observations are in agreement with a theoretical model. These results could be applicable to the population dynamics of other systems, such as the spread of disease in human populations coupled by migration.

Journal Article↗

PubMed2004

Dynamical epidemic suppression using stochastic prediction and control.

We consider the effects of noise on a model of epidemic outbreaks, where the outbreaks appear randomly. Using a constructive transition approach that predicts large outbreaks prior to their occurrence, we derive an adaptive control scheme that prevents large outbreaks from occurring. The theory is applicable to a wide range of stochastic processes with underlying deterministic structure.

Journal Article↗

PubMed2004

Stochastic bifurcation in a driven laser system: experiment and theory.

We analyze the effects of stochastic perturbations in a physical example occurring as a higher-dimensional dynamical system. The physical model is that of a class- B laser, which is perturbed stochastically with finite noise. The effect of the noise perturbations on the dynamics is shown to change the qualitative nature of the dynamics experimentally from a stochastic periodic attractor to one of chaoslike behavior, or noise-induced chaos. To analyze the qualitative change, we apply the technique of the stochastic Frobenius-Perron operator [L. Billings et al., Phys. Rev. Lett. 88, 234101 (2002)] to a model of the experimental system. Our main result is the identification of a global mechanism to induce chaoslike behavior by adding stochastic perturbations in a realistic model system of an optics experiment. In quantifying the stochastic bifurcation, we have computed a transition matrix describing the probability of transport from one region of phase space to another, which approximates the stochastic Frobenius-Perron operator. This mechanism depends on both the standard deviation of the noise and the global topology of the system. Our result pinpoints regions of stochastic transport whereby topological deterministic dynamics subjected to sufficient noise results in noise-induced chaos in both theory and experiment.

Journal Article↗

PubMed2004

Multi-scale continuum mechanics: from global bifurcations to noise induced high-dimensional chaos.

Many mechanical systems consist of continuum mechanical structures, having either linear or nonlinear elasticity or geometry, coupled to nonlinear oscillators. In this paper, we consider the class of linear continua coupled to mechanical pendula. In such mechanical systems, there often exist several natural time scales determined by the physics of the problem. Using a time scale splitting, we analyze a prototypical structural-mechanical system consisting of a planar nonlinear pendulum coupled to a flexible rod made of linear viscoelastic material. In this system both low-dimensional and high-dimensional chaos is observed. The low-dimensional chaos appears in the limit of small coupling between the continua and oscillator, where the natural frequency of the primary mode of the rod is much greater than the natural frequency of the pendulum. In this case, the motion resides on a slow manifold. As the coupling is increased, global motion moves off of the slow manifold and high-dimensional chaos is observed. We present a numerical bifurcation analysis of the resulting system illustrating the mechanism for the onset of high-dimensional chaos. Constrained invariant sets are computed to reveal a process from low-dimensional to high-dimensional transitions. Applications will be to both deterministic and stochastic bifurcations. Practical implications of the bifurcation from low-dimensional to high-dimensional chaos for detection of damage as well as global effects of noise will also be discussed.

Journal Article↗

PubMed2003

Constructing constrained invariant sets in multiscale continuum systems.

We present a method that we name the constrained invariant manifold method, a visualization tool to construct stable and unstable invariant sets of a map or flow, where the invariant sets are constrained to lie on a slow invariant manifold. The construction of stable and unstable sets constrained to an unstable slow manifold is exemplified in a singularly perturbed model arising from a structural-mechanical system consisting of a pendulum coupled to a viscoelastic rod. Additionally, we extend the step and stagger method [D. Sweet, H. Nusse, and J. Yorke, Phys. Rev. Lett. 86, 2261 (2001)] to calculate a delta pseudoorbit on a chaotic saddle constrained to the slow manifold in order to be able to compute the Lyapunov exponents of the saddle.

Journal Article↗

PubMed2003

Information flow dynamics and timing patterns in the arrival of email viruses.

Analysis of the timing of the arrival of email viruses at different computers provides a way of probing the structural and dynamical properties of the Internet. We found that the intervals t between the arrival of four different strains of email viruses have a power law distribution proportional to t(-d), where 1.5<or=d<or=3.2 and that there are positive correlations between these intervals. Salient features of the data were reproduced with a model having subnetwork units of different size where the structural components and the dynamical components all have power law scaling relationships with the size of the units. This is an assumption, that we hope will encourage empirical evaluation of these relationships.

Journal Article↗

PubMed2003

Approximating stable and unstable manifolds in experiments.

We introduce a procedure to reveal invariant stable and unstable manifolds, given only experimental data. We assume a model is not available and show how coordinate delay embedding coupled with invariant phase space regions can be used to construct stable and unstable manifolds of an embedded saddle. We show that the method is able to capture the fine structure of the manifold, is independent of dimension, and is efficient relative to previous techniques.

Journal Article↗

PubMed2003

Noise-induced unstable dimension variability and transition to chaos in random dynamical systems.

Results are reported concerning the transition to chaos in random dynamical systems. In particular, situations are considered where a periodic attractor coexists with a nonattracting chaotic saddle, which can be expected in any periodic window of a nonlinear dynamical system. Under noise, the asymptotic attractor of the system can become chaotic, as characterized by the appearance of a positive Lyapunov exponent. Generic features of the transition include the following: (1) the noisy chaotic attractor is necessarily nonhyperbolic as there are periodic orbits embedded in it with distinct numbers of unstable directions (unstable dimension variability), and this nonhyperbolicity develops as soon as the attractor becomes chaotic; (2) for systems described by differential equations, the unstable dimension variability destroys the neutral direction of the flow in the sense that there is no longer a zero Lyapunov exponent after the noisy attractor becomes chaotic; and (3) the largest Lyapunov exponent becomes positive from zero in a continuous manner, and its scaling with the variation of the noise amplitude is algebraic. Formulas for the scaling exponent are derived in all dimensions. Numerical support using both low- and high-dimensional systems is provided.

Journal Article↗

PubMed2002

Open-loop sustained chaos and control: a manifold approach.

We present a general method for preserving chaos in nonchaotic parameter regimes as well as preserving periodic behavior in chaotic regimes using a multifrequency phase control. The systems considered are nonlinear systems driven at a base frequency. Multifrequency phase control is defined as the addition of small subharmonic amplitude modulation coupled with a phase shift. By implementing multifrequency control, stable and unstable manifold intersections in postcrisis regimes may be manipulated to sustain chaos as well as to sustain periodic behavior. The theory and a preliminary experiment are demonstrated for a CO2 driven laser.

Journal Article↗

PubMed2002

Phase-space transport of stochastic chaos in population dynamics of virus spread.

A general way to classify stochastic chaos is presented and applied to population dynamics models. A stochastic dynamical theory is used to develop an algorithmic tool to measure the transport across basin boundaries and predict the most probable regions of transport created by noise. The results of this tool are illustrated on a model of virus spread in a large population, where transport regions reveal how noise completes the necessary manifold intersections for the creation of emerging stochastic chaos.

Algorithms↗

PubMed2002

Transition to chaos in continuous-time random dynamical systems.

We consider situations where, in a continuous-time dynamical system, a nonchaotic attractor coexists with a nonattracting chaotic saddle, as in a periodic window. Under the influence of noise, chaos can arise. We investigate the fundamental dynamical mechanism responsible for the transition and obtain a general scaling law for the largest Lyapunov exponent. A striking finding is that the topology of the flow is fundamentally disturbed after the onset of noisy chaos, and we point out that such a disturbance is due to changes in the number of unstable eigendirections along a continuous trajectory under the influence of noise.

Journal Article↗