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...

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...

Plasmodium of a cellular slime mould Physarum polycephalum is a very large eukaryotic microbe visible to the unaided eye. During its foraging behavior the plasmodium spans sources of nutrients with a network of protoplasmic tubes. In this paper we attempt to address the following question: Is...

We present methods and tools that can be used to study dynamic environmental resource management in a spatial setting, to explore spatially dependent regulation, and to understand pattern formation.In particular we present the maximum principle and its use in the context of the emerging frontier...

We study the nature of the instability of the homogeneous steady states of the subcritical real Ginzburg-Landau equation in the presence of group velocity. The shift of the absolute instability threshold of the trivial steady state, induced by the destabilizing cubic nonlinearities, is confirmed...

We present methods and tools that can be used to study dynamic environmental resource management in a spatial setting, to explore spatially dependent regulation, and to understand pattern formation. In particular, we present the maximum principle and its use in the context of the emerging...

A unified approach is proposed, which integrates game-theoretical models with models of directed motion. Specifically, strategic interactions in space and imitation of more successful neighboring strategies, as studied by spatial games, are combined with success-driven migration based on "test...