15 research outputs found
Memory Effects and Scaling Laws in Slowly Driven Systems
This article deals with dynamical systems depending on a slowly varying
parameter. We present several physical examples illustrating memory effects,
such as metastability and hysteresis, which frequently appear in these systems.
A mathematical theory is outlined, which allows to show existence of hysteresis
cycles, and determine related scaling laws.Comment: 28 pages (AMS-LaTeX), 18 PS figure
Hysteresis at low Reynolds number: the onset of 2D vortex shedding
Hysteresis has been observed in a study of the transition between laminar
flow and vortex shedding in a quasi-two dimensional system. The system is a
vertical, rapidly flowing soap film which is penetrated by a rod oriented
perpendicular to the film plane. Our experiments show that the transition from
laminar flow to a periodic K\'arm\'an vortex street can be hysteretic, i.e.
vortices can survive at velocities lower than the velocity needed to generate
them.Comment: RevTeX file 4 pages + 5 (encapsulated postscript) figures. to appear
in Phys.Rev.E, Rapid Communicatio
Traveling Waves in a Chain of Pulse-Coupled Oscillators
This article was published in the journal, Physical Review Letters [© American Physical Society]. It is also available at: http://link.aps.org/abstract/PRL/v80/p4815.We derive conditions for the existence of traveling wave solutions in a chain of pulse-coupled integrate-and-fire oscillators with nearest-neighbor interactions and distributed delays. A linear stability analysis of the traveling waves is carried out in terms of perturbations of the firing times of the oscillators. It is shown how traveling waves destabilize when the detuning between oscillators or the strength of the coupling becomes too large
Mechanisms of synchronization and pattern formation in a lattice of pulse-coupled oscillators
We analyze the physical mechanisms leading either to synchronization or to the formation of spatiotemporal patterns in a lattice model of pulse-coupled oscillators. In order to make the system tractable from a mathematical point of view we study a one-dimensional ring with unidirectional coupling. In such a situation, exact results concerning the stability of the fixed of the dynamic evolution of the lattice can be obtained. Furthermore, we show that this stability is the responsible for the different behaviors