Translationally invariant integro-differential equations are a common choice of model in neuroscience for describing the coarse-grained dynamics of cortical tissue. Here we analyse the propagation of travelling wavefronts in models of neural media that incorporate some form of modulation or randomness such that translational invariance is broken. We begin with a study of neural architectures in...

A hypergraph is k-irregular if there is no set of k vertices all of which have the same degree. We asymptotically determine the probability that a random uniform hypergraph is k-irregular.

A mathematical model of the spatio-temporal dynamics of a two host, two parasitoid system is presented. There is a coupling of the four species through parasitism of both hosts by one of the parasitoids. The model comprises a system of four reaction-diffusion equations. The underlying system of ordinary differential equations, modelling the host-parasitoid population dynamics, has a unique posi...

Similar to random sea waves, forces on the offshore structures due to waves are random. These forces can be mainly divided into two components, namely, inline forces and transverse or lift forces. The random nature of lift forces is more complicated than that of inline forces and both should be combined for design purposes. In the present paper, two different approaches have been used to determ...