We investigate activator–inhibitor systems in two spatial dimensions with a non-local coupling, for which the interaction strength decreases with the lattice distance as a power-law. By varying a single parameter we can pass from a local (Laplacian) to a global (all-to-all) coupling type. We...

A coupled map lattice model is proposed as a simple simulation model for growth patterns in a diffusion field. The numerical simulation in a one-dimensional coupled map lattice is consistent with the solution of the Stefan problem. Needle-like and dendritic patterns are obtained in...

We study the pattern dynamics in a reaction–diffusion model of the activator–inhibitor type in the oscillatory regime. We consider finite systems with partially absorptive boundary conditions analysing examples in different geometries in one and two dimensions. We observe that the boundary...

After a brief introduction we review the nonperturbative weak noise approach to the Kardar–Parisi–Zhang (KPZ) equation in one dimension. We argue that the strong coupling aspects of the KPZ equation are related to the existence of localized propagating domain walls or solitons representing...

We propose a new cellular automaton (CA) model, which reproduces isotropic time-evolution patterns observed in the Belousov–Zhabotinsky reaction. Although several CA models have been proposed exhibiting isotropic patterns of the reaction, most of them need complicated rules and a large number...

Bacteria have developed sophisticated modes of cooperative behavior to cope with unfavorable environmental conditions. Here we report the effect of antibiotic stress on the colonial development of Paenibacillus dendritiformis and P. vortex. We focus on the effect of co-trimoxazole on the...

Using a one parameter free energy model for surfactants, we numerically study the effects of hydrodynamics in the microemulsion and lamellar phases. Our results show that the dynamical correlation function has temporal oscillations for a range of hydrodynamical coupling strengths in the...

We study pattern formation in periodic systems with conserved dynamics driven by both thermally sustained flux and external (athermal) flux. Assuming the stochastic nature of each kind of flux we discuss noise induced patterning with competing stochastic dynamics in the framework of the...

Pedestrian counter flow is investigated by experiment and simulation. The experiment is performed for the channel with open boundaries. Two types of walkers, going to the right and to the left, are taken into account. The video recordings and measurements of individual arrival times are...

The dynamics of reaction-diffusion systems in low dimensions is often driven by fluctuations and a simple-minded description in terms of rate equations is not sufficient. Moreover, the emergence of complex patterns in such systems can involve simultaneously several new mechanisms as, for...