Propagation Failure in Excitable Media

We study a mechanism of pulse propagation failure in excitable media where stable traveling pulse solutions appear via a subcritical pitchfork bifurcation. The bifurcation plays a key role in that mechanism. Small perturbations, externally applied or from internal instabilities, may cause pulse propagation failure (wave breakup) provided the system is close enough to the bifurcation point. We derive relations showing how the pitchfork bifurcation is unfolded by weak curvature or advective field perturbations and use them to demonstrate wave breakup. We suggest that the recent observations of wave breakup in the Belousov-Zhabotinsky reaction induced either by an electric field or a transverse instability are manifestations of this mechanism.Comment: 8 pages. Aric Hagberg: http://cnls.lanl.gov/~aric; Ehud Meron:http://www.bgu.ac.il/BIDR/research/staff/meron.htm

Stratified spatiotemporal chaos in anisotropic reaction-diffusion systems

Numerical simulations of two dimensional pattern formation in an anisotropic bistable reaction-diffusion medium reveal a new dynamical state, stratified spatiotemporal chaos, characterized by strong correlations along one of the principal axes. Equations that describe the dependence of front motion on the angle illustrate the mechanism leading to stratified chaos

Controlling domain patterns far from equilibrium

A high degree of control over the structure and dynamics of domain patterns in nonequilibrium systems can be achieved by applying nonuniform external fields near parity breaking front bifurcations. An external field with a linear spatial profile stabilizes a propagating front at a fixed position or induces oscillations with frequency that scales like the square root of the field gradient. Nonmonotonic profiles produce a variety of patterns with controllable wavelengths, domain sizes, and frequencies and phases of oscillations.Comment: Published version, 4 pages, RevTeX. More at http://t7.lanl.gov/People/Aric

Breathing Spots in a Reaction-Diffusion System

A quasi-2-dimensional stationary spot in a disk-shaped chemical reactor is observed to bifurcate to an oscillating spot when a control parameter is increased beyond a critical value. Further increase of the control parameter leads to the collapse and disappearance of the spot. Analysis of a bistable activator-inhibitor model indicates that the observed behavior is a consequence of interaction of the front with the boundary near a parity breaking front bifurcation.Comment: 4 pages RevTeX, see also http://chaos.ph.utexas.edu/ and http://t7.lanl.gov/People/Aric

Order Parameter Equations for Front Transitions: Planar and Circular Fronts

Near a parity breaking front bifurcation, small perturbations may reverse the propagation direction of fronts. Often this results in nonsteady asymptotic motion such as breathing and domain breakup. Exploiting the time scale differences of an activator-inhibitor model and the proximity to the front bifurcation, we derive equations of motion for planar and circular fronts. The equations involve a translational degree of freedom and an order parameter describing transitions between left and right propagating fronts. Perturbations, such as a space dependent advective field or uniform curvature (axisymmetric spots), couple these two degrees of freedom. In both cases this leads to a transition from stationary to oscillating fronts as the parity breaking bifurcation is approached. For axisymmetric spots, two additional dynamic behaviors are found: rebound and collapse.Comment: 9 pages. Aric Hagberg: http://t7.lanl.gov/People/Aric/; Ehud Meron: http://www.bgu.ac.il/BIDR/research/staff/meron.htm

A Phase Front Instability in Periodically Forced Oscillatory Systems

Multiplicity of phase states within frequency locked bands in periodically forced oscillatory systems may give rise to front structures separating states with different phases. A new front instability is found within bands where $\omega_{forcing}/\omega_{system}=2n$ ($n>1$). Stationary fronts shifting the oscillation phase by $\pi$ lose stability below a critical forcing strength and decompose into $n$ traveling fronts each shifting the phase by $\pi/n$. The instability designates a transition from stationary two-phase patterns to traveling $n$-phase patterns

Multi-Phase Patterns in Periodically Forced Oscillatory Systems

Periodic forcing of an oscillatory system produces frequency locking bands within which the system frequency is rationally related to the forcing frequency. We study extended oscillatory systems that respond to uniform periodic forcing at one quarter of the forcing frequency (the 4:1 resonance). These systems possess four coexisting stable states, corresponding to uniform oscillations with successive phase shifts of $\pi/2$. Using an amplitude equation approach near a Hopf bifurcation to uniform oscillations, we study front solutions connecting different phase states. These solutions divide into two groups: $\pi$-fronts separating states with a phase shift of $\pi$ and $\pi/2$-fronts separating states with a phase shift of $\pi/2$. We find a new type of front instability where a stationary $\pi$-front ``decomposes'' into a pair of traveling $\pi/2$-fronts as the forcing strength is decreased. The instability is degenerate for an amplitude equation with cubic nonlinearities. At the instability point a continuous family of pair solutions exists, consisting of $\pi/2$-fronts separated by distances ranging from zero to infinity. Quintic nonlinearities lift the degeneracy at the instability point but do not change the basic nature of the instability. We conjecture the existence of similar instabilities in higher 2n:1 resonances (n=3,4,..) where stationary $\pi$-fronts decompose into n traveling $\pi/n$-fronts. The instabilities designate transitions from stationary two-phase patterns to traveling 2n-phase patterns. As an example, we demonstrate with a numerical solution the collapse of a four-phase spiral wave into a stationary two-phase pattern as the forcing strength within the 4:1 resonance is increased

Four-phase patterns in forced oscillatory systems

We investigate pattern formation in self-oscillating systems forced by an external periodic perturbation. Experimental observations and numerical studies of reaction-diffusion systems and an analysis of an amplitude equation are presented. The oscillations in each of these systems entrain to rational multiples of the perturbation frequency for certain values of the forcing frequency and amplitude. We focus on the subharmonic resonant case where the system locks at one fourth the driving frequency, and four-phase rotating spiral patterns are observed at low forcing amplitudes. The spiral patterns are studied using an amplitude equation for periodically forced oscillating systems. The analysis predicts a bifurcation (with increasing forcing) from rotating four-phase spirals to standing two-phase patterns. This bifurcation is also found in periodically forced reaction-diffusion equations, the FitzHugh-Nagumo and Brusselator models, even far from the onset of oscillations where the amplitude equation analysis is not strictly valid. In a Belousov-Zhabotinsky chemical system periodically forced with light we also observe four-phase rotating spiral wave patterns. However, we have not observed the transition to standing two-phase patterns, possibly because with increasing light intensity the reaction kinetics become excitable rather than oscillatory.Comment: 11 page

Effects of Prior Acute Exercise on Circulating Cytokine Concentration Responses to a High-fat Meal

High-fat meal consumption alters the circulating cytokine profile and contributes to cardiometabolic diseases. A prior bout of exercise can ameliorate the triglyceride response to a high-fat meal, but the interactive effects of exercise and high-fat meals on cytokines that mediate cardiometabolic risk are not fully understood. We investigated the effects of prior exercise on the responses of circulating tumor necrosis factor-a (TNF-a), interleukin-6 (IL-6), IL-8, leptin, retinol-binding protein 4 (RBP4), vascular endothelial growth factor (VEGF), basic fibroblast growth factor (bFGF), placental growth factor (PlGF), and soluble fms-like tyrosine kinase-1 (sFlt-1) to a high-fat meal. Ten healthy men were studied before and 4 h after ingestion of a high-fat meal either with or without ~50 min of endurance exercise at 70% of VO2 max on the preceding day. In response to the high-fat meal, lower leptin and higher VEGF, bFGF, IL-6, and IL-8 concentrations were evident (P \u3c 0.05 for all). There was no effect of the high-fat meal on PlGF, TNF-a, or RBP4 concentrations. We found lower leptin concentrations with prior exercise (P \u3c 0.05) and interactive effects of prior exercise and the high-fat meal on sFlt-1 (P \u3c 0.05). The high-fat meal increased IL-6 by 59% without prior exercise and 218% with prior exercise (P \u3c 0.05). In conclusion, a prior bout of endurance exercise does not affect all high-fat meal–induced changes in circulating cytokines, but does affect fasting or postprandial concentrations of IL-6, leptin, and sFlt-1. These data may reflect a salutary effect of prior exercise on metabolic responses to a high-fat meal

Complex Patterns in Reaction-Diffusion Systems: A Tale of Two Front Instabilities

Two front instabilities in a reaction-diffusion system are shown to lead to the formation of complex patterns. The first is an instability to transverse modulations that drives the formation of labyrinthine patterns. The second is a Nonequilibrium Ising-Bloch (NIB) bifurcation that renders a stationary planar front unstable and gives rise to a pair of counterpropagating fronts. Near the NIB bifurcation the relation of the front velocity to curvature is highly nonlinear and transitions between counterpropagating fronts become feasible. Nonuniformly curved fronts may undergo local front transitions that nucleate spiral-vortex pairs. These nucleation events provide the ingredient needed to initiate spot splitting and spiral turbulence. Similar spatio-temporal processes have been observed recently in the ferrocyanide-iodate-sulfite reaction.Comment: Text: 14 pages compressed Postscript (90kb) Figures: 9 pages compressed Postscript (368kb