Search results for "Pattern formation"

Arresting soliton collapse in two-dimensional nonlinear Schrödinger systems via spatiotemporal modulation of the external potential

2007

We predict stable, collapse-free solitonslike structures in two-dimensional nonlinear Schr\"odinger systems in subdiffractive regimes, accomplished by a spatiotemporal modulation of the external potential. We investigate the scaling laws, the stability, and the dynamical properties of these subdiffractive solitons.

Closed Busse balloon for rolls and skew-varicose instability in a Swift-Hohenberg model with nonlinear resonance

1998

Abstract A Swift-Hohenberg model incorporating a nonlinear resonance is shown to produce stable rolls only in a closed region of the parameter space. This Busse balloon is limited by zigzag and Eckhaus boundaries. A skew-varicose instability outside the balloon also exists. Implications with nonlinear optics and hydrodynamic convection are commented.

Minimal Absent Words in Rooted and Unrooted Trees

2019

We extend the theory of minimal absent words to (rooted and unrooted) trees, having edges labeled by letters from an alphabet \(\varSigma \) of cardinality \(\sigma \). We show that the set \(\text {MAW}(T)\) of minimal absent words of a rooted (resp. unrooted) tree T with n nodes has cardinality \(O(n\sigma )\) (resp. \(O(n^{2}\sigma )\)), and we show that these bounds are realized. Then, we exhibit algorithms to compute all minimal absent words in a rooted (resp. unrooted) tree in output-sensitive time \(O(n+|\text {MAW}(T)|)\) (resp. \(O(n^{2}+|\text {MAW}(T)|)\) assuming an integer alphabet of size polynomial in n.

Nonmonotonic Pattern Formation in Three Species Lotka-Volterra System with Colored Noise

2005

A coupled map lattice of generalized Lotka-Volterra equations in the presence of colored multiplicative noise is used to analyze the spatiotemporal evolution of three interacting species: one predator and two preys symmetrically competing each other. The correlation of the species concentration over the grid as a function of time and of the noise intensity is investigated. The presence of noise induces pattern formation, whose dimensions show a nonmonotonic behavior as a function of the noise intensity. The colored noise induces a greater dimension of the patterns with respect to the white noise case and a shift of the maximum of its area towards higher values of the noise intensity.

Topical issue on Ecological Complex Systems

2008

New degeneration of Fay's identity and its application to integrable systems

2011

In this paper, we find a new degenerated version of Fay's trisecant identity; this degeneration corresponds to the limit when the four points entering the trisecant identity coincide pairwise. This degenerated version of Fay's identity is used to construct algebro-geometric solutions to the multi-component nonlinear Schrodinger equation. This identity also leads to an independent derivation of algebro-geometric solutions to the Davey–Stewartson equations previously obtained in [17] in the framework of the Krichever scheme. We also give the condition of smoothness of the obtained solutions.

Unifying vectors and matrices of different dimensions through nonlinear embeddings

2020

Complex systems may morph between structures with different dimensionality and degrees of freedom. As a tool for their modelling, nonlinear embeddings are introduced that encompass objects with different dimensionality as a continuous parameter $\kappa \in \mathbb{R}$ is being varied, thus allowing the unification of vectors, matrices and tensors in single mathematical structures. This technique is applied to construct warped models in the passage from supergravity in 10 or 11-dimensional spacetimes to 4-dimensional ones. We also show how nonlinear embeddings can be used to connect cellular automata (CAs) to coupled map lattices (CMLs) and to nonlinear partial differential equations, derivi…

A C0-Semigroup of Ulam Unstable Operators

2020

The Ulam stability of the composition of two Ulam stable operators has been investigated by several authors. Composition of operators is a key concept when speaking about C0-semigroups. Examples of C0-semigroups formed with Ulam stable operators are known. In this paper, we construct a C0-semigroup (Rt)t&ge

Ulam Stability for the Composition of Operators

2020

Working in the setting of Banach spaces, we give a simpler proof of a result concerning the Ulam stability of the composition of operators. Several applications are provided. Then, we give an example of a discrete semigroup with Ulam unstable members and an example of Ulam stable operators on a Banach space, such that their sum is not Ulam stable. Another example is concerned with a C 0 -semigroup ( T t ) t &ge

Nonlinear dynamics of semiflexible magnetic filaments in an ac magnetic field

2006

Flexible spontaneously magnetized filaments exist in the living world (magnetotactic bacteria) and arise in magnetic colloids with large magnetodipolar interaction parameter. We demonstrate that these filaments possess variety of novel nonlinear phenomena in an ac magnetic field: orientation of the filament in the direction perpendicular to the field and the development of the oscillating U-like shapes, which presumably can lead to the formation of rings of magnetic filaments. It is found that these phenomena are determined by the development of the localized boundary modes of the filament deformation. We have illustrated by qualitative estimates that the phenomena found may be useful for i…