Related papers: Localized structures in coupled Ginzburg-Landau eq…
Motivated by the rich variety of complex patterns observed on the surface of fluid layers that are vibrated at multiple frequencies, we investigate the effect of such resonant forcing on systems undergoing a Hopf bifurcation to spatially…
The conditions are discussed for which an ensemble of interacting oscillators may demonstrate the Landau-Hopf scenario of successive birth of multi-frequency quasi-periodic motions. A model is proposed that is a network of five globally…
The periodic solutions of a type of nonlinear hyperbolic partial differential equations with a localized nonlinearity are investigated. For instance, these equations are known to describe several acoustical systems with fluid-structure…
We consider Complex Ginzburg-Landau equations with a polynomial nonlinearity in the real line. We use splitting-methods to prove well-posedness for a subset of almost periodic spaces. Specifically, we prove that if the initial condition has…
We develop a contact-geometric framework for dissipative nonlinear field theories by extending the least constraint theorem to complex fields and establishing a rigorous link with probability measures. The Complex Ginzburg-Landau Equation…
We introduce a numerical technique for controlling the location and stability properties of Hopf bifurcations in dynamical systems. The algorithm consists of solving an optimization problem constrained by an extended system of nonlinear…
The coupled Stuart-Landau equation serves as a fundamental model for exploring synchronization and emergent behavior in complex dynamical systems. However, understanding its dynamics from a comprehensive nonlinear perspective remains…
We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.
Gibbsian structure in random point fields has been a classical tool for studying their spatial properties. However, exact Gibbs property is available only in a relatively limited class of models, and it does not adequately address many…
Three coupled Ginzburg-Landau equations for hexagonal patterns with broken chiral symmetry are investigated. They are relevant for the dynamics close to onset of rotating non-Boussinesq or surface-tension-driven convection. Steady and…
The Complex Ginzburg-Landau equation is studied assuming a directed network of coupled oscillators. The asymmetry makes the spectrum of the Laplacian operator complex, and it is ultimately responsible for the onset of a generalized class of…
The propagation of stable coherent entities of an electromagnetic field in nonlinear media with parameters varying in space can be described in the framework of iterations of nonlinear integral transformations. It is shown that for a set of…
The dynamics of self-oscillatory extended systems, resonantly forced at a frequency close to that of the natural oscillations (1:1 resonance), is shown to be universally described by a complex Ginzburg-Landau equation containing an…
The cubic Complex Ginzburg-Landau Equation (CGLE) has a one parameter family of traveling localized source solutions. These so called 'Nozaki-Bekki holes' are (dynamically) stable in some parameter range, but always structually unstable: A…
Generalized contact bundles are odd dimensional analogues of generalized complex manifolds. They have been introduced recently and very little is known about them. In this paper we study their local structure. Specifically, we prove a local…
Bialgebras and Hopf (bi)modules are typical algebraic structures with several interacting operations. Their structural and homological study is therefore quite involved. We develop the machinery of braided systems, tailored for handling…
I consider the problem of self-oscillatory systems undergoing a homogeneous Hopf bifurcation when they are submitted to an external forcing that is periodic in time, at a frequency close to the system's natural frequency (1:1 resonance),…
We report the observation of different localized structures coexisting for the same parameter values in an extended system. The experimental findings are carried out in a nonlinear optical interferometer, and are fully confirmed by…
A variant of the complex Ginzburg-Landau equation is used to investigate the frequency locking phenomena in spatially extended systems. With appropriate parameter values, a variety of frequency-locked patterns including flats, $\pi$ fronts,…
The photoelectrodissolution of n-type silicon constitutes a convenient model system to study the nonlinear dynamics of oscillatory media. On the silicon surface, a silicon oxide layer forms. In the lateral direction, the thickness of this…