The phase shift between oscillations of blood pressure (BP) and Doppler middle cerebral artery flow velocity (MCAFV) reflects continuous cerebral autoregulatory action. It is not known whether a similar phase shift exists for cortical hemodynamics ('microvascular level') assessed by near infrared spectroscopy (NIRS) and what the effects are of pathological conditions. This study investigates th...

Using available signal (i.e., spectral and time-frequency) analysis methods, it can be difficult to detect neural oscillations because of their continuously changing properties (i.e., nonstationarities) and the noise in which they are embedded. Here, we introduce fractally scaled envelope modulation (FSEM) estimation which is sensitive specifically to the changing properties of oscillatory acti...

We consider a class of three dimensional, singularly perturbed predator-prey systems having two predators competing exploitatively for the same prey in a constant environment. By using dynamical systems techniques and the geometric singular perturbation theory, we give precise conditions which guarantee the existence of stable relaxation oscillations for systems within the class. Such result sh...

This paper presents qualitative and bifurcation analysis near the degenerate equilibrium in a two-stage cancer model of interactions between lymphocyte cells and solid tumor and contributes to a better understanding of the dynamics of tumor and immune system interactions. We first establish the existence of Hopf bifurcation in the 3-dimensional cancer model and rule out the occurrence of the de...

Polarized, stored beams are becoming a more and more important tool in nuclear and high energy physics. In order to measure the beam polarization in a storage ring the polarization vector of the stored, beam has to aim, revolution for revolution, over a period of seconds to minutes, into the same, so-called “stable”, direction. In this paper measurements at the Indiana University Cooler Ring (I...

We study chains of strongly electrically coupled relaxation oscillators modeling dopamine neurons. When individual oscillators are in the regime close to an Andronov–Hopf bifurcation (AHB), the coupled system exhibits a variety of oscillatory behavior. We show that the proximity of individual oscillators to the AHB has a significant impact on the system dynamics in a wide range of parameters. I...

there are several sources for pressure oscillations in solid propellant rocket motors. oscillatory flow field is one of them. free shear layers in motor flow field cause vortex shedding. end edges of propellant grains and baffle edge in two-segmented motors are samples of such zones. these vortices move from their forming points and strike the field walls. the kinetic energy of vortices change ...

A family of second-order, Lo-stable methods is developed and analysed for the numerical solution of the simple heat equation with time-dependent boundary conditions. Methods of the family need only real arithmetic in their implementation. In a series of numerical experiments no oscillations, which are a feature of some results obtained using Ao-stable methods, are observed in the computed solut...

We consider patterns formed by active transport of auxin in a tissue, where the accumulation of transporters is activated by local fluxes of auxin. We characterize the steady states for which auxin is homogeneous in the tissue. Under a condition of regularity of the dependence of transporters to the flux, we can prove that one of these steady states, with zero flux everywhere, is always locally...