Pattern formation in nonlinear complex systems is one of the central problems of the natural, social and technological sciences. In this paper, we consider a mathematical model of predator–prey interaction subject to self as well as cross-diffusion, arising in processes described by a system...

In this work we investigate the phenomena of pattern formation and wave propagation for a reaction–diffusion system with nonlinear diffusion. We show how cross-diffusion destabilizes uniform equilibrium and is responsible for the initiation of spatial patterns. Near marginal stability, through...

Flow and diffusion distributed structures (FDS) are stationary spatially periodic patterns that can be observed in reaction-diffusion-advection systems. These structures arise when the flow rate exceeds a certain bifurcation point provided that concentrations of interacting species at the inlet...

Noise-induced absolute instability is demonstrated in computer experiments with a one-dimensional reaction–diffusion system. This phenomenon may occur in spatially extended flow systems of different nature, when the parameters are chosen close to the point of transition from convective to...

Swimming bacteria of the species Bacillus subtilis require and consume oxygen. In static liquid cultures the cells' swimming behaviour leads them to accumulate up oxygen concentration gradients generated by consumption and supply. Since the density of bacterial cells exceeds that of the fluid in...

We show here different methods to demonstrate the intrinsic mobility of cavity solitons and realize a number of cavity soliton trajectories. These methods are based on one hand, on the drift of cavity solitons in phase or amplitude gradients and on the other hand, on the recently discovered...