A review of recent developments in the theoretical description and mathematical modelling of subdiffusion-reaction systems is presented. A number of subdiffusion-reaction models are discussed, including models of subdiffusion-limited reactions and models with intertwined subdiffusion and reaction operators. Specific features of the instability development and pattern formation are discussed. So...

The theoretical and practical understanding of cognitive development depends on working memory, the limited information temporarily accessible for such daily activities as language processing and problem solving. In this article, I assess many possible reasons that working memory performance improves with development. A first glance at the literature leads to the weird impression that working m...

Pattern formation via synchronization and oscillator death is considered in networks of diffusively coupled limit-cycle oscillators. Different examples of patterns and their dynamics are presented including nontrivial effects such as: (i) synchronized clusters induced by disorder and (ii) transitions from non-propagation to propagation of fronts via the intermittency. © 2002 IMACS. Published by...

A variety of two-dimensional fluid systems, known as dipole-mediated systems, exhibit a dipole-dipole interaction between their fluid constituents. The competition of this repulsive dipolar force with the cohesive fluid forces cause these systems to form intricate and patterned structures in their boundaries. In this thesis, we show that the microscopic details of any such system are irrelevant...

We introduce Process Algebra with Hooks (PA[H]). In PA[H] processes represent different layers of abstraction, from biochemistry to tissue, and special synchronisations via hook actions ensure consistency between these abstractions. There is an explicit representation of geometrical space and the algebra has a stochastic semantics based on functional rates of reactions.

The spatially distributed reaction networks are indispensable for the understanding of many important phenomena concerning the development of organisms, coordinated cell behavior, and pattern formation. The purpose of this brief discussion paper is to point out some open problems in the theory of PDE and compartmental ODE models of balanced reactiondiffusion networks.

Hebbian and competitive Hebbian algorithms are almost ubiquitous in modeling pattern formation in cortical development. We analyse in theoretical detail a particular model (adapted from Piepenbrock & Obermayer, 1999) for the development of Id stripe-like patterns, which places competitive and interactive cortical influences, and free and restricted initial arborisation onto a common footing.

We study the longitudinal motion of beam particles under the action of a single resonator wave induced by the beam itself. Based on the method of multiple scales we derive a system of coupled amplitude equations for the slowly varying part of the longitudinal distribution function and for the resonator wave envelope, corresponding to an arbitrary wave number. The equation governing the slow evo...

Over 60 years have passed since Alan Turing first postulated a mechanism for biological pattern formation. Although Turing did not have the chance to extend his theories before his unfortunate death two years later, his work has not gone unnoticed. Indeed, many researchers have since taken up the gauntlet and extended his revolutionary and counter-intuitive ideas. Here, we reproduce the basics ...

Turing's model of pattern formation has been extensively studied analytically and numerically, and there is recent experimental evidence that it may apply in certain chemical systems. The model is based on the assumption that all reacting species obey the same type of boundary condition pointwise on the boundary. We call these scalar boundary conditions. Here we study mixed or nonscalar boundar...