Related papers: Order Parameter Equations for Front Transitions: P…
The sunflower equation describes the motion of the tip of a plant due to the auxin transportation under the influence of gravity. This work proposes the fractional-order generalization to this delay differential equation. The equation…
This paper is concerned with the existence and qualitative properties of pulsating fronts for spatially periodic reaction-diffusion equations with bistable nonlinearities. We focus especially on the influence of the spatial period and,…
We present a novel general framework to deal with forward and backward components of the electromagnetic field in axially-invariant nonlinear optical systems, which include those having any type of linear or nonlinear transverse…
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…
The well-known cubic Allen-Cahn (AC) equation is a simple gradient dynamics (or variational) model for a nonconserved order parameter field. After revising main literature results for the occuring different types of moving fronts, we employ…
A symmetry breaking mechanism is shown to occur in an array composed of symmetric bistable Lorenz units coupled through a nearest neighbour scheme. When the coupling is increased, we observe the route: standing --> oscillating -->…
We study dense mixtures of passive and active self-aligning disks with isotropic or anisotropic mobility. We find that the passive fraction controls an order-disorder transition that is continuous in the isotropic case and discontinuous in…
In cosmological first-order phase transitions, the microscopic interaction of the phase transition fronts with non-equilibrium plasma particles manifests itself macroscopically as friction forces. In general, it is a nontrivial problem to…
In this paper mechanisms of reversion - momentum transition are considered. Two basic nonlinear mechanisms are highlighted: a slow and fast bifurcation. A slow bifurcation leads to the equilibrium evolution, preceded by stability loss delay…
Cell polarity and movement are fundamental to many biological functions. Experimental and theoretically studies have indicated that interactions of certain proteins lead to the cell polarization which plays a key role in controlling the…
Parametric oscillators are examples of externally driven systems that can exhibit two stable states with opposite phase depending on the initial conditions. In this work, we propose to study what happens when the external forcing is…
We study two new models of two particle species invading a surface from opposite sides. Collisions of particles of different species lead to the formation of congestion fronts. One of the models implements a reversible process whereas in…
We study the spatiotemporal properties of coherent states (peaks, holes, and fronts) in a bistable activator-inhibitor system that exhibits biochemical saturated autocatalysis, and in which fronts do not preserve spatial parity symmetry.…
Microscopic mechanisms of natural processes are frequently understood in terms of random walk models by analyzing local particle transitions. This is because these models properly account for dynamic processes at the molecular level and…
The dynamics of weak vs. strong first order phase transitions is investigated numerically for 2+1 dimensional scalar field models. It is argued that the change from a weak to a strong transition is itself a (second order) phase transition,…
We analyze the stability and dynamics of bistable planar fronts in multicomponent reaction-diffusion systems on $\mathbb{R}^{d}$. Under standard spectral stability assumptions, we establish Lyapunov stability of the front against fully…
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…
We consider a bound system of charged particles moving in an external electromagnetic field, including leading relativistic corrections. The difference from the point particle with a magnetic moment comes from the presence of…
In this article, we consider a class of bi-stable reaction-diffusion equations in two components on the real line. We assume that the system is singularly perturbed, i.e. that the ratio of the diffusion coefficients is (asymptotically)…
We study circle maps with a flat interval where the critical exponents at the two boundary points of the flat spot might be different. The space of such systems is partitioned in two connected parts whose common boundary only depends on the…