Travelling Waves in Plankton Dynamics

tiring instability and travelling waves in diffusive plankton models with delayed nutrient recycling

In this paper we propose a reaction-diffusion system with two distributed delays to stimulate the growth of plankton communities in the lakes/oceans in which the plankton feeds on a limiting nutrient supplied at a constant rate. The limiting nutrient is partially recycled after the death of the organisms and a distributed delay is used to model nutrient recycling. The second delay is involved i...

Travelling Waves in Continuum/discrete Bistable/monostable Dynamics

Traveling waves play a key role in mathematical models since they characterize observable fundamental phenomena in nature. A typical traveling wave corresponds to a state which is time independent (in some cases time periodic) in a moving coordinates. In a one space dimensional setting, it depends only on z := x − ct where c is the wave speed and x and t are respectively space and time variable...

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