Solitary travelling auto-waves in fractional reaction–diffusion systems

Travelling Waves for Reaction-diffusion-convection Systems

(1) ut = Auxx + f(u), u ∈ R , x ∈ R, t ∈ [0,∞), where A is a real, positive-definite, N × N matrix and f : R → R is a continuously differentiable nonlinear function. The vector u may represent, for example, the concentrations of chemicals or the population densities of interacting species, the interactions between components of u being modelled by the reaction term f(u) and their diffusion by A...

Periodic travelling waves in cyclic predator-prey systems

Jonathan A. Sherratt Centre for Theoretical Modelling in Medicine, Department of Ma thema tie, Heriot-Watt University, Edinburgh EH14 4AS, U.K. E-mail: jasbma.hw.ac.uk Abstract Predation is an established cause of cycling in prey species. Here, the ability of predation to explain periodic travelling waves in prey populations, which have recently been found in a number of spatiotemporal field st...

Travelling waves in multivortex configurations

We investigate zero modes of a multivortex background which are due to the energetic degeneracy of the planar static n-vortex solution in Bogomol’nyi limit of the Abelian Higgs model parametrised by a set of 2n real parameters. The zero modes take the form of waves travelling with a speed of light independently along each of the vortices irrespectively to their mutual separations. String descri...

Synaptic travelling waves

An important goal of neuroscience is to establish a series of direct links between the abstract nature of biophysical model equations and their interpretation in terms of experimental findings in biological neural networks. I propose to address this issue by developing a novel mathematical analysis of the dynamics of synaptically interacting neural systems and by establishing a framework for co...

Stability of Travelling Waves