Related papers: Scroll waves in isotropic excitable media : linear…
We consider the stability of periodic gravity free-surface water waves traveling downstream at a constant speed over a shear flow of finite depth. In case the free surface is flat, a sharp criterion of linear instability is established for…
A stability of nearly limiting Stokes waves to superharmonic perturbations is considered numerically. The new, previously inaccessible branches of superharmonic instability were investigated. Our numerical simulations suggest that…
Euler's equations govern the behavior of gravity waves on the surface of an incompressible, inviscid, and irrotational fluid of arbitrary depth. We investigate the spectral stability of sufficiently small-amplitude, one-dimensional Stokes…
Two-dimensional statistically stationary isotropic turbulence with an imposed uniform scalar gradient is investigated. Dimensional arguments are presented to predict the inertial range scaling of the turbulent scalar flux spectrum in both…
We investigate the instabilities and bifurcations of traveling pulses in a model excitable medium; in particular we discuss three different scenarios for the loss of stability resp. the disappearance of stable pulses. In numerical…
Spatial variations in the electrical properties of cardiac tissue can occur because of cardiac diseases. We introduce such gradients into mathematical models for cardiac tissue and then study, by extensive numerical simulations, their…
The paper addresses the bistability caused by spontaneous symmetry breaking bifurcation in a one-dimensional periodically corrugated nonlinear waveguide pumped by coherent light at normal incidence. The formation and the stability of the…
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…
We study a Rock-Paper-Scissors model for competing populations that exhibits travelling waves in one spatial dimension and spiral waves in two spatial dimensions. A characteristic feature of the model is the presence of a robust…
Identification and extraction of vortical structures and of waves in a disorganised flow is a mayor challenge in the study of turbulence. We present a study of the spatio-temporal behavior of turbulent flows in the presence of different…
Possibility of asymmetric square convection is investigated numerically using a few mode Lorenz-like model for thermal convection in Boussinesq fluids confined between two stress free and conducting flat boundaries. For relatively large…
A large class of multidimensional nonlinear Schroedinger equations admit localized nonradial standing wave solutions that carry nonzero intrinsic angular momentum. Here we provide evidence that certain of these spinning excitations are…
A switching dynamical system by means of piecewise linear systems in R^3 that presents multistability is presented. The flow of the system displays multiple scroll attractors due to the unstable hyperbolic focus-saddle equilibria with…
Rotating spiral and scroll waves (vortices) are investigated in the FitzHugh-Nagumo model of excitable media. The focus is on a parameter region in which there exists bistability between alternative stable vortices with distinct periods.…
Although internal gravity waves are generally recognized as an important mechanism to distribute energy through the atmosphere, their dynamics near the instability is only partially understood to date. Many types of instabilities, notably…
We consider principal properties of various wave regimes in two selected excitable systems with linear cross-diffusion in one spatial dimension observed at different parameter values. This includes fixed-shape propagating waves, envelope…
Abnormal electrical activity from the boundaries of ischemic cardiac tissue is recognized as one of the major causes in generation of ischemia-reperfusion arrhythmias. Here we present theoretical analysis of the waves of electrical activity…
The equations for waves on the surface of an irrotational incompressible fluid are derived in the coordinates of the velocity potential/stream function. The low frequency shallow water approximation for these waves is derived for a varying…
Spiral waves in two-dimensional excitable media have been observed experimentally and studied extensively. It is now well-known that the symmetry properties of the medium of propagation drives many of the dynamics and bifurcations which are…
Spiral waves are self-repeating waves that can form in excitable media, propagating outward from their center in a spiral pattern. Spiral waves have been observed in different natural phenomena and have been linked to medical conditions…