Learn More
In this article, we analyze traveling waves in a reaction–diffusionmechanics (RDM) system. The system consists of a modified FitzHugh–Nagumo equation, also known as the Aliev–Panfilov model, coupled bidirectionally with an elasticity equation for a deformable medium. In one direction, contraction and expansion of the elastic medium decreases and increases,(More)
In a diffusive geophysical flow, there is not a single timescale or unique pathway for passive scalar transport from the reservoir’s surface into the interior because of irreversible diffusive mixing processes. Instead, there is a range of pathways and hence a transit-time distribution (TTD) since last surface contact. We explore the issues that arise when(More)
We investigate the problem of attractor reconstruction from interspike times produced by an integrate-and-fire model of neuronal activity. Suzuki et. al. [14] found that the reconstruction of the Rössler attractor is incomplete if the integrate-and-fire model is used. We explain this failure using two observations. One is that the attractor reconstruction(More)
It is known [8, 11, 16, 26] that phase locking can entrain frequency information when the leaky integrate-and-fire (IF) model of a neuron is forced by a periodic function. We show that this is still the case when the IF model is made more biologically realistic. We incorporate into our model spike dependent threshold modulation and refractory periods.(More)
This article is concerned with pointwise growth and spreading speeds in systems of parabolic partial differential equations. Several criteria exist for quantifying pointwise growth rates. These include the location in the complex plane of singularities of the pointwise Green’s function and pinched double roots of the dispersion relation. The primary aim of(More)
The purpose of this paper is to explore spatio-temporal pattern formation via invasion fronts in the one and two dimensional Keller-Segel chemotaxis model. In the one-dimensional case, simulations show that solutions that begin near an unstable equilibrium evolve into periodic patterns. These in turn evolve into new patterns through a process known as(More)
We study wavespeed selection in a staged invasion process. That is, we study a model in which an unstable homogeneous state is replaced via an invading front with a secondary state. This secondary state is also unstable and, in turn, replaced by a stable homogeneous state via a secondary invasion front. In particular, we are interested in the selected(More)