Complex organizing centers in groups of oscillatory particles.

We investigate the origin and evolution of spatiotemporal complexity in a system of locally coupled Belousov-Zhabotinsky chemical oscillators. Using a combination of high resolution microscopy and fine grain numerical modeling, we demonstrate that the behavior arises from an initial phase heterogeneity of the oscillators. This heterogeneity produces wave breaks in the system with the free ends becoming pinned to holes in the medium. The fastest of these pinned tips behave as reentrant circuits that phase set the rest of the medium. The slower tips are repeatedly destroyed and then re-created by the central circuit. The resulting spatiotemporal pattern repeats with the frequency of the reentrant circuit, with its spatial structure depending on the location of the initial wave breaks.

Spatial symmetry breaking in the Belousov-Zhabotinsky reaction with light-induced remote communication.

Domains containing spiral waves form on a stationary background in a photosensitive Belousov-Zhabotinsky reaction with light-induced alternating nonlocal feedback. Complex behavior of colliding and splitting wave fragments is found with feedback radii comparable to the spiral wavelength. A linear stability analysis of the uniform stationary states in an Oregonator model reveals a spatial symmetry breaking instability. Numerical simulations show behavior in agreement with that found experimentally and also predict a variety of other new patterns.

Wave propagation in subexcitable media with periodically modulated excitability.

Wave propagation in a photosensitive, subexcitable Belousov-Zhabotinsky medium is made possible by periodic modulation of a homogeneous illumination field. The propagation can be understood in terms of an interplay between the radial expansion of the wave and the motion of its free ends as the excitability varies periodically. This description leads to a simple kinematic analysis that provides insights into the initial conditions and forcing parameters giving rise to sustained wave propagation.

Experimental and theoretical studies of feedback stabilization of propagating wave segments.

Experimental and theoretical studies of the excitability boundary for spiral wave behavior are presented. The boundary is defined by unstable wave segments, which are stabilized by using a negative-feedback control algorithm. A kinematic description of the constant-size, constant-shape wave segments is presented.

Coherent structure analysis of spatiotemporal chaos

We introduce a measure to quantify spatiotemporal turbulence in extended systems. It is based on the statistical analysis of a coherent structure decomposition of the evolving system. Applied to a cellular excitable medium and a reaction-diffusion model describing the oxidation of CO on Pt(100), it reveals power-law scaling of the size distribution of coherent space-time structures for the state of spiral turbulence. The coherent structure decomposition is also used to define an entropy measure, which sharply increases in these systems at the transition to turbulence.

Self-segregation of competitive chaotic populations

The dynamical behavior of species competing for a common resource is studied with a reaction-diffusion system based on cubic autocatalysis. Randomly seeded populations self-segregate to form a complex network of domains separated by distinct interfaces. For chaotic populations in one-dimensional media, the interfaces exhibit irregular motions on long time scales. In two-dimensional media, the interface motions are governed by curvature-induced drift.

Uncertain destination dynamics.

Certain dynamical systems exhibit a sensitivity to initial conditions in which the asymptotic state is selected from an infinite number of possible states. The phase space of such systems is foliated with "attractors," each of which is associated with a particular set of initial conditions. The associated uncertain destination dynamics can be analyzed by an appropriate reduction of the full system to a subsystem that explicitly yields the dynamics.

Noise sustained waves in subexcitable media: From chemical waves to brain waves.

We discuss a novel type of spatiotemporal pattern that can be observed in subexcitable media when coupled to a thermal environment. These patterns have been recently observed in several different types of systems: a subexcitable photosensitive Belousov-Zhabotinsky reaction, hippocampal slices of rat brains, and astrocyte syncytium. In this paper, we introduce the basic concepts of subexcitable media, describe recent experimental observations in chemistry and neurophysiology, and put these observation into context with computer simulations. (c) 1998 American Institute of Physics.

Anisotropy and spiral organizing centers in patterned excitable media.

Chemical wave behavior in a patterned Belousov-Zhabotinsky system prepared by printing the catalyst of the reaction on membranes with an ink jet printer is described. Cellular inhomogeneities give rise to global anisotropy in wave propagation, with specific local patterns resulting in hexagonal, diamond, and pentagonal geometries. Spiral wave sources appear spontaneously and serve as organizing centers of the surrounding wave activity. The experimental methodology offers flexibility for studies of excitable media with made-to-order spatial inhomogeneities.

Navigating complex labyrinths: optimal paths from chemical waves.

The properties of excitable media are exploited to find minimum-length paths in complex labyrinths. Optimal pathways are experimentally determined by the collection of time-lapse position information on chemical waves propagating through mazes prepared with the Belousov-Zhabotinsky reaction. The corresponding velocity fields provide maps of optimal paths from every point in an image grid to a particular target point. Collisions of waves that were temporarily separated by obstacles mark boundary lines between Significantly different paths with the same absolute distance. The pathfinding algorithm is tested in very complex mazes with a simple reaction-diffusion model.