Journal ArticleDOI
Patterns and coherence resonance in the stochastic Swift–Hohenberg equation with Pyragas control: The Turing bifurcation case
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TLDR
In this article, a multiple time scales analysis for the Swift-Hohenberg equation with delayed feedback via Pyragas control, with and without additive noise, is provided, where the delay can drive the appearance of an additional time scale, intermediate to the usual slow and fast time scales observed in the modulation of rolls without delay.About:
This article is published in Physica D: Nonlinear Phenomena.The article was published on 2018-02-15. It has received 14 citations till now. The article focuses on the topics: Swift–Hohenberg equation & Context (language use).read more
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Stability of Travelling Waves for Reaction-Diffusion Equations with Multiplicative Noise
TL;DR: In this paper, a semigroup approach was developed to handle the nonlinear stability question in a fashion that is closely related to modern deterministic methods, and a semilinear sPDE was obtained by applying a stochastic phase shift together with a time-transform.
Spontaneous motion of cavity solitons induced by a delayed feedback
TL;DR: In this paper, the authors studied the properties of 2D cavity solitons in a coherently driven optical resonator subjected to a delayed feedback and derived an analytical formula for the speed of a moving soliton.
Journal ArticleDOI
State-dependent act-and-wait time-delayed feedback control algorithm
TL;DR: The TDFC is modified by appending the feedback loop with a state-dependent switch, which allows to reduce the phase space dimension of time-delayed feedback systems and to significantly simplify the theory.
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The impact of multiplicative noise in SPDEs close to bifurcation via amplitude equations
Dirk Blömker,Hongbo Fu +1 more
TL;DR: In this paper, an amplitude equation was derived to describe the dynamics of the bifurcating pattern of a stochastic Ginzburg-Landau equation with a cubic nonlinearity perturbed by a general multiplicative noise that preserves the constant trivial solution.
References
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Journal ArticleDOI
Pattern formation outside of equilibrium
Michael Cross,P. C. Hohenberg +1 more
TL;DR: A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented in this article, with emphasis on comparisons between theory and quantitative experiments, and a classification of patterns in terms of the characteristic wave vector q 0 and frequency ω 0 of the instability.
Journal ArticleDOI
On the Lambert W function
TL;DR: A new discussion of the complex branches of W, an asymptotic expansion valid for all branches, an efficient numerical procedure for evaluating the function to arbitrary precision, and a method for the symbolic integration of expressions containing W are presented.
Book
Spectral Methods in MATLAB
TL;DR: This paper presents a meta-analyses of Chebyshev differentiation matrices using the DFT and FFT as a guide to solving fourth-order grid problems.
Journal ArticleDOI
Continuous control of chaos by self-controlling feedback
TL;DR: In this paper, the stabilization of unstable periodic orbits of a chaotic system is achieved either by combined feedback with the use of a specially designed external oscillator, or by delayed self-controlling feedback without using of any external force.
Journal ArticleDOI
A test for normality of observations and regression residuals
Carlos M. Jarque,Anil K. Bera +1 more
TL;DR: In this paper, the Lagrange multiplier procedure or score test on the Pearson family of distributions was used to obtain tests for normality of observations and regression disturbances, and the tests suggested have optimum asymptotic power properties and good finite sample performance.
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