The Fisher equation, which combines di/usive motion of individuals with nonlinearities arising from their growth and competition processes, is analyzed, generalized, and applied to the dynamics of bacteria, pattern formation, and the spread of epidemics. Analytic solutions are also presented for some exactly soluble and physically relevant variants of the equation. c © 2004 Elsevier B.V. All ri...

The dynamical characteristics of a single isolated Hopfield-type neuron with dissipation and time-delayed self-interaction under periodic stimuli are studied. Sufficient conditions for the heteroassociative stable encoding of periodic external stimuli are obtained. Both discrete and continuously distributed delays are included.

Topics covered: 1. What is disturbance? 2. Characteristics of disturbances and disturbance regimes 3. Role of disturbance in ecosystems and landscapes 4. Factors affecting disturbances 5. Feedback mechanisms affecting disturbance regimes 6. Interactions among the physical template, biotic processes and disturbance regimes 7. Human effects on disturbance regimes 8. Resource management implications.

We derive a rigorous scaling law for minimizers in a natural version of the regularized Cross-Newell model for pattern formation far from threshold. These energyminimizing solutions support defects having the same character as what is seen in experimental studies of the corresponding physical systems and in numerical simulations of the microscopic equations that describe these systems.

We analyze pattern formation in doubly resonant intracavity second-harmonic generation in the presence of competing nondegenerate parametric downconversion. We show that for positive cavity detuning of the fundamental frequency the threshold for parametric oscillation is lower than that of transverse, pattern forming instabilities. The parametric oscillation strongly modifies the pattern dynami...

Shear-thickening behavior and shear-induced pattern formation have been observed in semidilute starch solutions. While the shear-thickening behavior is due to breaking up of highly concentrated gel-like structures dispersed in dilute starch solutions, the pattern-forming behavior is not well understood. The pattern formation, observed when the starch solution is exposed to a high shear field, i...

We seek to understand patterns that form due to acute inflammation in the skin in the absence of specific pathogenic stimuli. By incorporating inhibition (represented by an anti-inflammatory cytokine) into a classical Keller–Segel chemotaxis model, we create a novel model that produces a variety of spatial patterns. We find that the dynamical instability in both homogeneous and nonhomogeneous s...

A new approach for the theoretical description of structure formation in acoustic avitation is developed. The model consists of two coupled partial differential equations describing the spatiotemporal evolution of the sound field amplitude and the bubble concentration. Linear stability analysis and numerical simulation• of the pattern formation are presented. The relation between this approach ...

Algorithms Design for pattern formation is an interesting science and many investigations are done about it. In this paper, a novel pattern formation method using asynchronous cellular automata for generating square Kufic patterns is explored. Square Kufic is a kind of script that is used in many Islamic architecture buildings. In our new method, cellular automata rules causing a specified kind...

The downscaling of frequently-acquired geostationary Land Surface Temperature (LST) data can compensate the lack of high spatiotemporal LST data for urban climate studies. In order to be usable, the generated datasets must accurately reproduce the spatiotemporal features of the coarse-scale LST time series with greater spatial detail. This work concerns this issue and exploits the high temporal...