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...

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...

We consider a hierarchical set of dynamical systems, each of which may support individual pattern formation processes. In the limit case of weak top-down interactions it provides a suitable framework for the design of self-organizing scenarios both from constructional and evolutionary...