Dynamic scaling laws in two types of extended Hamiltonian systems at dissipation onset
The transition to dissipation in one-dimensional extended Hamiltonian systems with saddle-node bifurcations of stationary solutions is characterized. Three different systems are studied: (i) nonlinear Schrödinger flow past a localized obstacle; (ii) ...
Shock bowing and vorticity dynamics during propagation into different transverse density profiles
A 2D numerical investigation is presented of shock wave propagation into a gas whose density is modulated in the transverse direction across the width of a shock tube. These density modulations represent temperature distributions in which low density ...
Mean flow in hexagonal convection: stability and nonlinear dynamics
Weakly nonlinear hexagon convection patterns coupled to mean flow are investigated within the framework of coupled Ginzburg-Landau equations. The equations are in particular relevant for non-Boussinesq Rayleigh-Bénard convection at low Prandtl numbers. ...
Global solution of the pressureless gas equation with viscosity
We construct a global weak solution to a d-dimensional system of zero-pressure gas dynamics modified by introducing a finite artificial viscosity. We use discrete approximations to the continuous gas and make particles move along trajectories of the ...
Synchrony, stability, and firing patterns in pulse-coupled oscillators
We study non-trivial firing patterns in small assemblies of pulse-coupled oscillatory maps. We find conditions for the existence of waves in rings of coupled maps that are coupled bi-directionally. We also find conditions for stable synchrony in general ...
The evolution of synaptically generated waves in one- and two-dimensional domains
We study the onset and evolution of waves in an integrate-and-fire network of synaptically coupled neurons in one- and two-dimensional domains which are restricted to firing one spike. We determine the critical size of initial excitation of the network ...
Synchronization likelihood: an unbiased measure of generalized synchronization in multivariate data sets
The study of complex systems consisting of many interacting subsystems requires the use of analytical tools which can detect statistical dependencies between time series recorded from these subsystems. Typical examples are the electroencephalogram (EEG) ...