Bacterial species Bacillus subtilis is known to exhibit various colony patterns, depending on the substrate softness and nutrient concentration. We have examined the self-affinity and roughness exponent α for growing interfaces of colonies which belong to regions B (Eden-like) and D (disk-like)...

We introduce a cellular-automaton based model for the description of the migration and growth patterns of colonies of Bacillus subtilis. The two phases, associated with processes of migration and proliferation, are described by appropriate rules for the update of the automaton. We show that it...

The individual based simulator, INDividual DIScrete SIMulations (INDISIM) has been used to study the behaviour of the growth of bacterial colonies on a finite dish. The simulations reproduce the qualitative trends of pattern formation that appear during the growth of Bacillus subtilis on an agar...

This paper extends Turing analysis to standard recursive optimal control frameworks in economics and applies it to dynamic bioeconomic problems where the interaction of coupled economic and ecological dynamics under optimal control over space creates (or destroys) spatial heterogeneity. We show...

We consider a two-dimensional model of three species in rock-paper-scissors competition and study the self-organisation of the population into fascinating spiraling patterns. Within our individual-based metapopulation formulation, the population composition changes due to cyclic dominance...

Spatial evolutionary games model individuals who are distributed in a spatial domain and update their strategies upon playing a normal form game with their neighbors. We derive integro-differential equations as deterministic approximations of the microscopic updating stochastic processes. This...

This paper presents a fairly general treatment of recursive infinite horizon forward looking optimizing systems on infinite dimensional spatial domains. It includes optimal control, an analysis of local stability of spatially flat optimal steady states and development of techniques to compute...

This paper adapts Turing analysis and applies it to dynamic bioeconomic problems where the interaction of coupled economic and ecological dynamics over space endogenously creates (or destroys) spatial heterogeneity. We examine the emergence of traveling wave solutions in open access fishery...

The coarsening of an array of vortex ripples prepared in an unstable state is discussed within the framework of a simple mass transfer model first introduced by K. H. Andersen et al. (see Ref. 1). Two scenarios for the selection of the final pattern are identified. When the initial state is...

The formation of complex patterns in chemical systems is discussed in the following cases: relations of pattern formation to thermodynamics theories; unusually complex pattern formation in very simple experimental chemical systems; and numerical simulation of patterns that develop in...