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Formation of spatially localized oscillations in parametrically driven systems is studied, focusing on the dominant 2:1 resonance tongue. Both damped and self-exciting oscillatory media are considered. Near the primary subharmonic instability such systems are described by the forced complex Ginzburg-Landau equation. The technique of spatial dynamics is used(More)
Excitable cells can exhibit complex patterns of oscillations, such as spiking and bursting. In cardiac cells, pathological voltage oscillations, called early afterdepolarizations (EADs), have been widely observed under disease conditions, yet their dynamical mechanisms remain unknown. Here, we show that EADs are caused by Hopf and homoclinic bifurcations.(More)
Deficiency of matrix GLA protein (MGP), an inhibitor of bone morphogenetic protein (BMP)-2/4, is known to cause arterial calcification and peripheral pulmonary artery stenosis. Yet the vascular role of MGP remains poorly understood. To further investigate MGP, we created a new MGP transgenic mouse model with high expression of the transgene in the lungs.(More)
A mesoscale fluid film placed on a solid support may break up and form droplets. In addition, droplets may exhibit spontaneous translation by modifying the wetting properties of the substrate, resulting in asymmetry in the contact angles. We examine mechanisms for droplet formation and motion on uniform and terraced landscapes, i.e., composite substrates.(More)
Experiments on a quasi-two-dimensional Belousov–Zhabotinsky (BZ) reaction-diffusion system, periodically forced at approximately twice its natural frequency, exhibit resonant labyrinthine patterns that develop through two distinct mechanisms. In both cases, large amplitude labyrinthine patterns form that consist of interpenetrating fingers of(More)
The formation of oscillons in a synchronously oscillating background is studied in the context of both damped and self-exciting oscillatory media. Using the forced complex Ginzburg-Landau equation we show that such states bifurcate from finite amplitude homogenous states near the 2:1 resonance boundary. In each case we identify a region in parameter space(More)
We present a theoretical study of nonlinear pattern selection mechanisms in a model of bounded reaction-diffusion-advection system. The model describes the activator-inhibitor type dynamics of a membrane reactor characterized by a differential advection and a single diffusion; the latter excludes any finite wave number instability in the absence of(More)
Pattern formation mechanisms of a reaction-diffusion-advection system, with one diffusivity, differential advection, and (Robin) boundary conditions of Danckwerts type, are being studied. Pattern selection requires mapping the domains of coexistence and stability of propagating or stationary nonuniform solutions, which for the general case of far from(More)
Actin-based cellular protrusions are an ubiquitous feature of cells, performing a variety of critical functions ranging from cell-cell communication to cell motility. The formation and maintenance of these protrusions relies on the transport of proteins via myosin motors, to the protrusion tip. While tip-directed motion leads to accumulation of motors (and(More)
A distinct propagation of solitary waves in the presence of autocatalysis, diffusion, and symmetry-breaking (differential) advection, is being studied. These pulses emerge at lower reaction rates of the autocatalytic activator, i.e., when the advective flow overcomes the fast excitation and induces a fluid type "drifting" behavior, making the phenomenon(More)