We analyze the dynamics of neural oscillators in the presence of both synaptic and diffusive coupling. First we derive a computationally effective, yet plausible model of extra-synaptic neurotransmitter diffusion. Second, we modify the Hindmarsh-Rose oscillator to account for the diffusion. For ensembles of these modified model neurons we obtain conditions ensuring global synchronization. Our r...

A classical theory is proposed to describe the non-RRKM effects in activated asymmetric top triatomic molecules observed numerically in classical molecular dynamics simulations of ozone. The Coriolis coupling is shown to result in an effective diffusive energy exchange between the rotational and vibrational degrees of freedom. A stochastic differential equation is obtained for the K-component o...

This paper concerns the analysis of approximations of transport equations in diffusive media. Firstly, we consider a variational formulation for the first-order transport equation that has the correct diffusive behavior in the limit of small mean free paths. The associated bilinear form is shown to be coercive on a classical Hilbert space in transport theory with a constant of coercivity indepe...

The study of a fractional Burgers equation arising in nonlinear acoustics is presented. The motivation comes from an elementary model of shock waves in brass wind instruments, that proves useful in musical acoustics. Such a model results from the coupling of a conservative nonlinear system with a dissipative term; here the dissipation is represented by a fractional derivative in time, for which...

Transient wave forms in neural networks with diffusive and nonlocal coupling have attracted particular interest because they may mediate recruitment of healthy cortical tissue into a pathological state during migraine. To investigate this process, we use a reaction-diffusion system of inhibitor-activator type as a generic model of pathological wave propagation and set it close to bifurcation in...

We investigate the spin dynamics and relaxation in remotely doped two dimensional electron systems where the dopants lead to random fluctuations of the Rashba spin-orbit coupling. Due to the resulting random-spin precession, the spin-relaxation time is limited by the strength and spatial scale of the random contribution to the spin-orbit coupling. We concentrate on the role of the randomness fo...

Networks of weakly nonlinear oscillators are considered with diffusive and timedelayed coupling. Averaging theory is used to determine parameter ranges for which the network experiences amplitude death, whereby oscillations are quenched and the equilibrium solution has a large domain of attraction. The amplitude death is shown to be a common phenomenon, which can be observed regardless of the p...

Ordinarily, two different topologies have been used to model spatiotemporal chaos and to study complexity in networks of maps: one where sites interact only with nearest neighbors (e.g., the standard diffusive coupling) and one where sites interact with all sites in the network (global coupling). Here we investigate intermediate regimes considering the interaction range as a free tunable parame...

It has been shown previously that identical spiking cells, incapable of bursting by themselves, may burst under weak diffusive coupling conditions. With stronger coupling, the coupled system reverts to bursting can be recovered by introducing heterogeneity in the model parameters. For a two-cell system, we explain the phenomenon with bifurcation analysis. For larger clusters of coupled cells, w...

We study spin dependent phonomena in superconducting junctions in both ballistic and diffusive regimes. For ballistic junctions we study both ferromagnet / sand d-wave superconductor junctions and two dimensional electron gas / s-wave superconductor junctions with Rashba spin-orbit coupling. It is shown that the exchange field alway suppresses the conductance while the Rashba spin-orbit couplin...