The scaling behavior of nonlocal surface growth equations are analyzed using a Flory-type approach introduced by Hentschel and Family [Phys. Rev. Lett. 66 (1991) 1982]. The growth equations studied include the nonlocal Kardar–Parisi–Zhang, nonlocal Sun–Guo–Grant, and nonlocal Lai–Das...

A one-dimensional reaction–diffusion model consisting of two species of particles and vacancies on a ring is introduced. The number of particles in one species is conserved while in the other species it can fluctuate because of creation and annihilation of particles. It has been shown that the...

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 discuss recently developed methods of studying long-time properties of initially separated reaction–diffusion systems with a reversible reaction of type A+B⇌C, including both analytical and numerical techniques.

In an earlier study [J.C. Lewis, H. Wheeler, Physica A 271 (1999) 63–86] of the dependence on jump probability p of the rates of diffusion-controlled reactions on simple cubic lattices in dimension 2≤d≤4 we found that the dependence was non-linear, which is not in accord with what would be...

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...

In this paper, the adaptive synchronization and lag synchronization are considered for uncertain dynamical system with time delay based on parameter identification and a novel control method is then further given using the Lyapunov functional method. With this new and effective method, parameter...

This paper deals with the synchronization problem of the recurrent neural networks with time-varying and distributed time-varying delays. Based on the drive–response concept, LMI approach and the Lyapunov stability theorem, a delay-dependent feedback controller is derived to achieve the...