Noise-supported travelling waves in sub-excitable media

Noise-induced Brownian motion of spiral waves

We study the erratic displacement of spiral waves forced to move in a medium with random spatiotemporal excitability. Analytical work and numerical simulations are performed in relation to a kinematic scheme, assumed to describe the autowave dynamics for weakly excitable systems. Under such an approach, the Brownian character of this motion is proved and the corresponding dispersion coefficient is evaluated. This quantity shows a nontrivial dependence on the temporal and spatial correlation parameters of the external fluctuations. In particular, a resonantlike behavior is neatly evidenced in terms of the noise correlation time for the particular situation of spatially uniform fluctuations. Actually, this case turns out to be, to a large extent, exactly solvable, whereas a pair of dispersion mechanisms are discussed qualitatively and quantitatively to explain the results for the more general scenario of spatiotemporal disorder.

Noise to order

Patterns in natural systems abound, from the stripes on a zebra to ripples in a riverbed. In many of these systems, the appearance of an ordered state is not unexpected as the outcome of an underlying ordered process. Thus crystal growth, honeycomb manufacture and floret evolution generate regular and predictable patterns. Intrinsically noisy and disordered processes such as thermal fluctuations or mechanically randomized scattering generate surprisingly similar patterns. Here we discuss some of the underlying mechanisms believed to be at the heart of these similarities.

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.

Compartmentalized reaction-diffusion systems

Reaction-diffusion systems consisting of a collection of reactive domains separated by chemically inactive regions are considered. The reactive dynamics is governed by a multistep reaction mechanism and each reactive domain is specific to a particular elementary step or collection of elementary steps of the global reaction mechanism. Far-from-equilibrium situations where the global kinetics can give rise to complex states such as bistability or oscillations are studied. A general method for the calculation of the average concentration on each reactive domain is presented. The effects of compartmentalization are illustrated by a study of the influence of diffusion, reactive domain size, and domain distribution on the nature of the stationary states of the Schlögl model. Compartmentalization can drive the system into and out of the bistable regime of this reactive system.

Disorder can eliminate oscillator death

We use an array of diffusively coupled limit-cycle oscillators with a regular monotonic trend of natural frequencies to demonstrate that the disorder introduced in the form of random deviations from a linear trend of frequencies can weaken considerably desynchronization-induced oscillator death and, as a result, increase oscillation intensity substantially. There exist definite optimal levels of magnitude of spatial disorder at which maximal oscillatory energy is attained in the array.

Resonantly forced inhomogeneous reaction-diffusion systems

The dynamics of spatiotemporal patterns in oscillatory reaction-diffusion systems subject to periodic forcing with a spatially random forcing amplitude field are investigated. Quenched disorder is studied using the resonantly forced complex Ginzburg-Landau equation in the 3:1 resonance regime. Front roughening and spontaneous nucleation of target patterns are observed and characterized. Time dependent spatially varying forcing fields are studied in the 3:1 forced FitzHugh-Nagumo system. The periodic variation of the spatially random forcing amplitude breaks the symmetry among the three quasi-homogeneous states of the system, making the three types of fronts separating phases inequivalent. The resulting inequality in the front velocities leads to the formation of "compound fronts" with velocities lying between those of the individual component fronts, and "pulses" which are analogous structures arising from the combination of three fronts. Spiral wave dynamics is studied in systems with compound fronts. (c) 2000 American Institute of Physics.

Lifetime enhancement of scroll rings by spatiotemporal fluctuations

The dynamics of three-dimensional scroll rings with spatiotemporal random excitability is investigated numerically using the FitzHugh-Nagumo model. Depending on the correlation time and length scales of the fluctuations, the lifetime of the ring filament is enlarged and a resonance effect between the time scale of the scroll ring and the time correlation of the noise is observed. Numerical results are interpreted in terms of a simplified stochastic model derived from the kinematical equations for three-dimensional excitable waves.

Human electroencephalogram induces transient coherence in excitable spatiotemporal chaos

A time series from a human electroencephalogram (EEG) is used as a local perturbation to a reaction-diffusion model with spatiotemporal chaos. For certain finite ranges of amplitude and frequency it is observed that the strongly irregular perturbations can induce transient coherence in the chaotic system. This could be interpreted as "on-line" detection of an inherently correlated pattern embedded in the EEG.

Noise sustained propagation: local versus global noise

We expand on prior results on noise supported signal propagation in arrays of coupled bistable elements. We present and compare experimental and numerical results for kink propagation under the influence of local and global fluctuations. As demonstrated previously for local noise, an optimum range of global noise power exists for which the medium acts as a reliable transmission "channel." We discuss implications for propagation failure in a model of cardiac tissue, and present a general theoretical framework based on discrete kink statistics. Valid for generic bistable chains, the theory captures the essential features observed in our experiments and numerical simulations.

Noise-aided control of chaotic dynamics in a logistic map

Controlling chaos involves employing small perturbations to a control parameter, resulting in the stabilization of the system (naturally chaotic) on one of the infinite unstable periodic orbits embedded in the chaotic attractor. In this Brief Report we study the constructive role of external noise in increasing the efficiency of controlling chaos. Using a logistic map as an example, control of chaotic dynamics is achieved using a linear delayed-feedback strategy. Working in the subthreshold regime of control (where the value of control constant is less than the minimum value required to stabilize the period-1 target state), system dynamics in the presence of superimposed noise (system plus control plus noise) exhibit a resonance effect. Furthermore it is observed that the time required to reach the target state decreases appreciably in the presence of an optimum level of noise.

Noise-induced memory in extended excitable systems

We describe a form of memory exhibited by extended excitable systems driven by stochastic fluctuations. Under such conditions, the system self-organizes into a state characterized by power-law correlations, thus retaining long-term memory of previous states. The exponents are robust and model independent. We discuss implications of these results for the functioning of cortical neurons as well as for networks of neurons.

Brownian motion of spiral waves driven by spatiotemporal structured noise

Spiral chemical waves subjected to a spatiotemporal random excitability are experimentally and numerically investigated in relation to the light-sensitive Belousov-Zhabotinsky reaction. Brownian motion is identified and characterized by an effective diffusion coefficient which shows a rather complex dependence on the time and length scales of the noise relative to those of the spiral. A kinematically based model is proposed whose results are in good qualitative agreement with experiments and numerics.

Her name is "Lucy", our three-million-year-old ancestor

Dental anthropology is a key discipline in studies to determine the evolutionary history of our hominid ancestors, to identify the origin and dispersal of modern humans, and to reconstruct the source of observed dental variation. A survey of hominid and modern human evolutionary history, emphasizing results from powerful multivariate dental morphometric methodologies, suggests a single African origin of modern humans > 150,000 years before present from a Homo heidelbergensis ancestor. A continuum among modern humanity is described, with, first, sub-Saharan Africans, then southeast Asian Negrito, and Australian aborigines at its extant root. Other interpretations of the available data are possible. Examinations of the progress of the evolution of teeth through time give significant insight into dental morphogenetics and variation, and the biology of dental evolution. The mechanisms of evolution which fashion a phenotype and the methods of molecular and dental phylogenetics are reviewed and evaluated. This is an exciting time for dental anthropology, with fascinating and challenging questions to address, but anthropologists, not dentists, dominate the field. The perspective of a dentist can meaningfully add to the dynamics of dental anthropology.

Noise-induced phase separation: mean-field results

We present a study of a phase-separation process induced by the presence of spatially correlated multiplicative noise. We develop a mean-field approach suitable for conserved-order-parameter systems and use it to obtain the phase diagram of the model. Mean-field results are compared with numerical simulations of the complete model in two dimensions. Additionally, a comparison between the noise-driven dynamics of conserved and nonconserved systems is made at the level of the mean-field approximation.

Stochastic resonance in extended bistable systems: the role of potential symmetry

We study the role of potential symmetry in a three-field reaction-diffusion system presenting bistability by means of a two-state theory for stochastic resonance in general asymmetric systems. By analyzing the influence of different parameters in the optimization of the signal-to-noise ratio, we observe that this magnitude always increases with the symmetry of the system's potential, indicating that it is this feature which governs the optimization of the system's response to periodic signals.

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.