Biomedical subjects

Raymond Kapral

Publications and source records attributed to Raymond Kapral.

10 recordsLinked to original sources

PubMed2003

Rapid convergence of time-averaged frequency in phase synchronized systems.

Numerical and experimental evidences are presented to show that many phase synchronized systems of nonidentical chaotic oscillators, where the chaotic state is reached through a period-doubling cascade, show rapid convergence of the time-averaged frequency. The speed of convergence toward the natural frequency scales as the inverse of the measurement period. The results also suggest an explanation for why such chaotic oscillators can be phase synchronized.

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PubMed2003

Front explosions in three-dimensional resonantly-forced oscillatory systems.

Interface dynamics in a three-dimensional coupled map lattice with a period-3 local map is studied. The system possesses a parameter regime where one typically finds three-phase patterns consisting of spatially uniform domains which follow the period-3 cycle and oscillate among the three different phases. The interfaces where these domains meet may exhibit complex irregular dynamics. The system also has a parameter regime of "turbulent" dynamics, which is a chaotic transient with a superexponentially long lifetime. The transition from the three-phase pattern regime to the turbulent regime is studied. As a control parameter is tuned, the interfaces between domains develop turbulent structure. The thickness of the turbulent zone remains finite up to a critical parameter value after which it is infinite. We characterize this "front explosion" transition in three-dimensional systems and compare it with the analogous transition in two-dimensional systems where the critical properties are markedly different. The front explosion in the three-dimensional resonantly-forced complex Ginzburg-Landau equation is also investigated briefly and its character differs from that in the three-dimensional coupled map lattice.

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PubMed2003

Defect-mediated turbulence in systems with local deterministic chaos.

Defect-mediated turbulence is shown to exist in media where the underlying local dynamics is deterministically chaotic. While many of the characteristics of defect-mediated turbulence, such as the exponential decay of correlations and a squared Poissonian distribution for the number of defects, are identical to those seen in oscillatory media, the fluctuations in the number of defects differ significantly. The power spectra suggest the existence of underlying correlations that lead to a different and nonuniversal scaling structure in chaotic media.

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PubMed2002

Phase synchronization and topological defects in inhomogeneous media.

The influence of topological defects on phase synchronization and phase coherence in two-dimensional arrays of locally coupled, nonidentical, chaotic oscillators is investigated. The motion of topological defects leads to a breakdown of phase synchronization in the vicinities of the defects; however, the system is much more phase coherent as long as the coupling between the oscillators is strong enough to prohibit the continuous dynamical creation and annihilation of defects. The generic occurrence of topological defects in two and higher dimensions implies that the concept of phase synchronization has to be modified for these systems.

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PubMed2002

Oscillatory and chaotic dynamics in compartmentalized geometries.

The effects of spatial compartmentalization of a multistep reaction mechanism (Willamowski-Rössler model) whose mass action rate law shows oscillations and chaotic dynamics are explored. The mechanism is decomposed into subsets of reactions that are then assumed to take place in distinct regularly or randomly distributed spatial domains in the system. The reactive domains are coupled by diffusion. The spatiotemporal system states are investigated as a function of the system size and geometrical arrangement of the domains. A compartmentalization is chosen where the isolated domain attractors are simple steady states. It is then shown that changes in the system size or domain geometry can produce bifurcations leading to simple or period-doubled oscillatory attractors as well as chaotic states. These bifurcations are analyzed by direct simulations of the compartmentalized reaction-diffusion equations and by an analysis in terms of integral equations.

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PubMed2001

Scroll waves in spherical shell geometries.

The evolution of scroll waves in excitable media with spherical shell geometries is studied as a function of shell thickness and outer radius. The motion of scroll wave filaments that are the locii of phaseless points in the medium and organize the wave pattern is investigated. When the inner radius is sufficiently large the filaments remain attached to both the inner and outer surfaces. The minimum size of the sphere that supports spiral waves and the maximum number of spiral waves that can be sustained on a sphere of given size are determined for both regular and random initial distributions. When the inner radius is too small to support spiral waves the filaments detach from the inner surface and form a curved filament connecting the two spiral tips in the surface. In certain parameter domains the filament is an arc of a circle that shrinks with constant shape. For parameter values close to the meandering border, the filament grows and collisions with the sphere walls lead to turbulent filament dynamics. (c) 2001 American Institute of Physics.

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PubMed2000

Asynchronous algorithm for integration of reaction-diffusion equations for inhomogeneous excitable media.

An asynchronous algorithm for the integration of reaction-diffusion equations for inhomogeneous excitable media is described. Since many physical systems are inhomogeneous where either the local kinetics or the diffusion or conduction properties vary significantly in space, integration schemes must be able to account for wide variations in the temporal and spatial scales of the solutions. The asynchronous algorithm utilizes a fixed spatial grid and automatically adjusts the time step locally to achieve an efficient simulation where the errors in the solution are controlled. The scheme does not depend on the specific form of the local kinetics and is easily applied to systems with complex geometries. (c) 2000 American Institute of Physics.

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PubMed1994

Spatiotemporal intermittency on fractal lattices.

The transition to turbulence via spatiotemporal intermittency is investigated for coupled maps defined on generalized Sierpinski gaskets, a class of deterministic fractal lattices. Critical exponents that characterize the onset of intermittency are computed as a function of the fractal dimension of the lattice. Windows of spatiotemporal intermittency are found as the coupling parameter is varied for lattices with a fractal dimension greater than two. This phenomenon is associated with a collective chaotic behavior of the fractal array of coupled maps.

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PubMed1992

Coupled maps and pattern formation on the Sierpinski gasket.

The bifurcation structure of coupled maps on the Sierpinski gasket is investigated. The fractal character of the underlying lattice gives rise to stability boundaries for the periodic synchronized states with unusual features and spatially inhomogeneous states with a complex structure. The results are illustrated by calculations on coupled quadratic and cubic maps. For the coupled cubic map lattice bistability and domain growth processes are studied.

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PubMed1991

Vortex dynamics in oscillatory chemical systems.

Vortex core dynamics is studied in the Brusselator both near to and far from the Hopf bifurcation line for random and pair initial conditions. Extensive simulations are carried out for a pair of counter-rotating vortices close to the Hopf bifurcation line. Provided the vortices are not so far apart that wave-front annihilation produces strong gradients between their centers, the simulation results compare favorably with theories based on the complex Ginzburg-Landau equation. Far from the Hopf line the vortex core dynamics changes character and phenomena such as periodic motion of the vortex centers arise.

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