Biomedical subjects

Edward Ott

Publications and source records attributed to Edward Ott.

At least 37 records · Page 2Linked to original sources

PubMed2004

Growing networks with geographical attachment preference: emergence of small worlds.

We introduce a simple mechanism for the evolution of small world networks. Our model is a growing network in which all connections are made locally to geographically nearby sites. Although connections are made purely locally, network growth leads to stretching of old connections and to high clustering. Our results suggest that the abundance of small world networks in geographically constrained systems is a natural consequence of system growth and local interactions.

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PubMed2004

Communication with a chaotic traveling wave tube microwave generator.

Traveling wave tubes (TWTs) are vacuum electronic amplifiers (see Beck, Gittins, and Pierce) that are commonly used for communication in the centimeter wavelength range. Increasing demand for high data flow in wireless communication systems (satellite communication systems are a good example) raises needs for making TWT's more compact and efficient. Motivated by this we suggest a scheme in which a TWT with feedback is operated in a highly nonlinear regime where the device behaves chaotically. The chaos is controlled using small controls. Then, at the receiving end a receiving TWT synchronizes to the chaotic transmitter and amplifies the received signal with nearly no distortion. Results on numerical simulations of the proposed scheme are reported and used to evaluate its effectiveness.

Communication↗

PubMed2004

Localized error bursts in estimating the state of spatiotemporal chaos.

We consider the problem of estimating the current state of an evolving spatiotemporally chaotic system from noisy observations of the system state and a model of the system dynamics. Using a simple scheme for state estimation, we show the possible occurrence of temporally and spatially intermittent large bursts in the estimation error. We discuss the similarity of these bursts with those occurring at the bubbling transition in the synchronization of low dimensional chaotic dynamical systems. We characterize the spatial and temporal behavior of the bursts and investigate how the behavior changes as we vary the number and location of the observations.

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PubMed2003

Scaling properties of saddle-node bifurcations on fractal basin boundaries.

We analyze situations where a saddle-node bifurcation occurs on a fractal basin boundary. Specifically, we are interested in what happens when a system parameter is slowly swept in time through the bifurcation. Such situations are known to be indeterminate in the sense that it is difficult to predict the eventual fate of an orbit that tracks the prebifurcation node attractor as the system parameter is swept through the bifurcation. In this paper we investigate the scaling of (1) the fractal basin boundary of the static (i.e., unswept) system near the saddle-node bifurcation, (2) the dependence of the orbit's final destination on the sweeping rate, (3) the dependence of the time it takes for an attractor to capture a swept orbit on the sweeping rate, and (4) the dependence of the final attractor capture probability on the noise level. With respect to noise, our main result is that the effect of noise scales with the 5/6 power of the parameter drift rate. Our approach is to first investigate all these issues using one-dimensional map models. The simplification of treatment inherent in one dimension greatly facilitates analysis and numerical experiment, aiding us in obtaining the new results listed above. Following our one-dimensional investigations, we explain that these results can be applied to two-dimensional systems. We show, through numerical experiments on a periodically forced second-order differential equation example, that the scalings we have found also apply to systems that result in two-dimensional maps.

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PubMed2003

Dynamical origin for the occurrence of asynchronous hyperchaos and chaos via blowout bifurcations.

We investigate the dynamical origin for the occurrence of asynchronous hyperchaos and chaos via blowout bifurcations in coupled chaotic systems. An asynchronous hyperchaotic or chaotic attractor with a positive or negative second Lyapunov exponent appears through a blowout bifurcation. It is found that the sign of the second Lyapunov exponent of the newly born asynchronous attractor, exhibiting on-off intermittency, is determined through competition between its laminar and bursting components. When the "strength" (i.e., a weighted second Lyapunov exponent) of the bursting component is larger (smaller) than that of the laminar component, an asynchronous hyperchaotic (chaotic) attractor appears.

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PubMed2003

Pattern formation in a monolayer of magnetic spheres.

Pattern formation is investigated for a vertically vibrated monolayer of magnetic spheres. The spheres of diameter D encase cylindrical magnetic cores of length l. For large D/l, we find that the particles form a hexagonal-close-packed pattern in which the particles' dipole vectors assume a macroscopic circulating vortical pattern. For smaller D/l, the particles form concentric rings. The static configurational magnetic energy (which depends on D/l) appears to be a determining factor in pattern selection even though the experimental system is driven and dissipative.

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PubMed2003

Mechanism for the intermittent route to strange nonchaotic attractors.

Intermittent strange nonchaotic attractors (SNAs) appear typically in quasiperiodically forced period-doubling systems. As a representative model, we consider the quasiperiodically forced logistic map and investigate the mechanism for the intermittent route to SNAs using rational approximations to the quasiperiodic forcing. It is found that a smooth torus transforms into an intermittent SNA via a phase-dependent saddle-node bifurcation when it collides with a new type of "ring-shaped" unstable set.

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PubMed2003

Fractal properties of robust strange nonchaotic attractors in maps of two or more dimensions.

We consider the existence of robust strange nonchaotic attractors in a simple class of quasiperiodically forced systems. Rigorous results are presented demonstrating that the resulting attractors are strange in the sense that their box-counting dimension D0 is larger than their information dimension D1 by 1 (i.e., D(0)=D(1)+1). We also show how this property is manifested in numerical experiments.

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PubMed2003

Anomalous diffusion in infinite horizon billiards.

We consider the long time dependence for the moments of displacement <|r|(q)> of infinite horizon billiards, given a bounded initial distribution of particles. For a variety of billiard models we find <|r|(q)> approximately t(gamma(q)) (up to factors of ln t). The time exponent, gamma(q), is piecewise linear and equal to q/2 for q<2 and q-1 for q>2. We discuss the lack of dependence of this result on the initial distribution of particles and resolve apparent discrepancies between this time dependence and a prior result. The lack of dependence on initial distribution follows from a remarkable scaling result that we obtain for the time evolution of the distribution function of the angle of a particle's velocity vector.

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PubMed2003

Statistics and characteristics of spatiotemporally rare intense events in complex Ginzburg-Landau models.

We study the statistics and characteristics of rare intense events in two types of two-dimensional complex Ginzburg-Landau (CGL) equation based models. Our numerical simulations show finite amplitude collapselike solutions which approach the infinite amplitude solutions of the nonlinear Schrödinger equation in an appropriate parameter regime. We also determine the probability distribution function of the amplitude of the CGL solutions, which is found to have enhanced (as compared to Gaussian) probability for the amplitude to be large. Our results suggest a general picture in which an incoherent background of weakly interacting waves, occasionally, "by chance," initiates intense, coherent, self-reinforcing, highly nonlinear events.

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PubMed2003

Bifurcation scenarios for bubbling transition.

Dynamical systems with chaos on an invariant submanifold can exhibit a type of behavior called bubbling, whereby a small random or fixed perturbation to the system induces intermittent bursting. The bifurcation to bubbling occurs when a periodic orbit embedded in the chaotic attractor in the invariant manifold becomes unstable to perturbations transverse to the invariant manifold. Generically the periodic orbit can become transversely unstable through a pitchfork, transcritical, period-doubling, or Hopf bifurcation. In this paper a unified treatment of the four types of bubbling bifurcation is presented. Conditions are obtained determining whether the transition to bubbling is soft or hard; that is, whether the maximum burst amplitude varies continuously or discontinuously with variation of the parameter through its critical value. For soft bubbling transitions, the scaling of the maximum burst amplitude with the parameter is derived. For both hard and soft transitions the scaling of the average interburst time with the bifurcation parameter is deduced. Both random (noise) and fixed (mismatch) perturbations are considered. Results of numerical experiments testing our theoretical predictions are presented.

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PubMed2002

Long time algebraic relaxation in chaotic billiards.

The long-time algebraic relaxation process in spatially periodic billiards with infinite horizon is shown to display a self-similar time-asymptotic form. This form is identical for a class of such billiards, but can be different in an important special case.

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PubMed2002

Evolving networks with multispecies nodes and spread in the number of initial links.

We consider models for growing networks incorporating two effects not previously considered: (i) different species of nodes, with each species having different properties (such as different attachment probabilities to other node species) and (ii) when a new node is created, its number of links to old nodes is random with a given probability distribution. Our numerical simulations show good agreement with analytic solutions. As an application of our model, we investigate the movie-actor network with movies considered as nodes and actors as links.

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PubMed2002

Phase synchronization of chaotic attractors in the presence of two competing periodic signals.

We discuss the situation where two periodic signals compete to phase synchronize a chaotic attractor. Depending on the relative position of the periods with respect to the synchronization tongue for a single frequency signal, we distinguish several different cases. We find that, depending on parameters, it is possible that one or the other signal will entrain exclusively, or that they will entrain alternately, at their average frequency, or not at all.

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PubMed2000

Power spectrum of passive scalars in two dimensional chaotic flows.

In this paper the power spectrum of passive scalars transported in two dimensional chaotic fluid flows is studied theoretically. Using a wave-packet method introduced by Antonsen et al., several model flows are investigated, and the fact that the power spectrum has the k(-1)-scaling predicted by Batchelor is confirmed. It is also observed that increased intermittency of the stretching tends to make the roll-off of the power spectrum at the high k end of the k(-1) scaling range more gradual. These results are discussed in light of recent experiments where a k(-1) scaling range was not observed. (c) 2000 American Institute of Physics.

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PubMed2000

Stalactite basin structure of dynamical systems with transient chaos in an invariant manifold.

Dynamical systems with invariant manifolds occur in a variety of situations (e.g., identical coupled oscillators, and systems with a symmetry). We consider the case where there is both a nonchaotic attractor (e.g., a periodic orbit) and a nonattracting chaotic set (or chaotic repeller) in the invariant manifold. We consider the character of the basins for the attracting nonchaotic set in the invariant manifold and another attractor not in the invariant manifold. It is found that the boundary separating these basins has an interesting structure: The basin of the attractor not in the invariant manifold is characterized by thin cusp shaped regions ("stalactites") extending down to touch the nonattracting chaotic set in the invariant manifold. We also develop theoretical scalings applicable to these systems, and compare with numerical experiments. (c) 2000 American Institute of Physics.

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PubMed1997

Targeting in Hamiltonian systems that have mixed regular/chaotic phase spaces.

The problem of directing a trajectory of a chaotic dynamical system to a target has been previously considered, and it has been shown that chaos allows targeting using only small controls. In this paper we consider targeting in a Hamiltonian system, whose phase space contains a mixture of regular quasi-periodic and chaotic regions. A multistep forward-backward method targeting strategic intermediate points is found to be efficient and robust. It takes full advantage of the phase space structure and is believed to yield optimal transport times. It is robust under the influence of small noise and small modeling errors and recovers from temporary loss of control. Two illustrative examples, the standard map and the restricted circular three body problem, are presented. (The latter corresponds to motion of a space probe in the presence of the earth and the moon.) Comparisons are made of our method to other targeting strategies. (c) 1997 American Institute of Physics.

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PubMed1993

Chaotic scattering: An introduction.

In recent years chaotic behavior in scattering problems has been found to be important in a host of physical situations. Concurrently, a fundamental understanding of the dynamics in these situations has been developed, and such issues as symbolic dynamics, fractal dimension, entropy, and bifurcations have been studied. The quantum manifestations of classical chaotic scattering is also an extremely active field, with new analytical techniques being developed and with experiments being carried out. This issue of Chaos provides an up-to-date survey of the range of work in this important field of study.

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