Dynamics of Turing Patterns under Spatiotemporal Forcing

Rüdiger, Stephan; Míguez, David G.; Muñuzuri, Alberto P.; Sagués, Francesc; Casademunt, Jaume

doi:10.1103/physrevlett.90.128301

Cited by 86 publications

(83 citation statements)

References 19 publications

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“…In the last decade the focus of research has been shifted to the study of the formation of spatio-temporal patterns. Such spatio-temporal structures have been observed in chemical experiments (Perraud et al (1993); Rüdiger et al (2003)). Theoretical studies prove their existence for the Brusselator model (Rovinsky and Menzinger (1992)), in optical systems (Tlidi et al (1997)) and in semiconductor heterostructures (Just et al (2001)).…”

Section: Introductionmentioning

confidence: 58%

Instabilities in spatially extended predator–prey systems: Spatio-temporal patterns in the neighborhood of Turing–Hopf bifurcations

Baurmann

Groß

Feudel

2007

Journal of Theoretical Biology

327

218

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We investigate the emergence of spatio-temporal patterns in ecological systems. In particular we study a generalized predator-prey system on a spatial domain. On this domain diffusion is considered as the principal process of motion. We derive the conditions for Hopf and Turing instabilities without specifying the predatorprey functional responses and discuss their biological implications. Furthermore, we identify the codimension-2 Turing-Hopf bifurcation and the codimension-3 TuringTakens-Bogdanov bifurcation. These bifurcations give rise to complex pattern formation processes in their neighborhood. Our theoretical findings are illustrated with a specific model. In simulations a large variety of different types of long-term behavior, including homogenous distributions, stationary spatial patterns and complex spatio-temporal patterns is observed.

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Section: Introductionmentioning

confidence: 58%

Instabilities in spatially extended predator–prey systems: Spatio-temporal patterns in the neighborhood of Turing–Hopf bifurcations

Baurmann

Groß

Feudel

2007

Journal of Theoretical Biology

327

218

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“…During the past few years, attention had mostly focused on resonances or locking of spatially structured states, either oscillatory or stationary, under purely temporal [1][2][3] or spatial (steady) modulations [4 -7]. We extended these scenarios recently by proposing a particularly simple mode of spatiotemporal forcing [8]. The situation considered was the dynamical response of a striped Turing pattern to a resonant stripe modulation of a control parameter, sweeping the system at small velocities.…”

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confidence: 99%

Traveling-Stripe Forcing Generates Hexagonal Patterns

et al. 2004

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We study the response of Turing stripe patterns to a simple spatiotemporal forcing. This forcing has the form of a traveling wave and is spatially resonant with the characteristic Turing wavelength. Experiments conducted with the photosensitive chlorine dioxide-iodine-malonic acid reaction reveal a striking symmetry-breaking phenomenon of the intrinsic striped patterns giving rise to hexagonal lattices for intermediate values of the forcing velocity. The phenomenon is understood in the framework of the corresponding amplitude equations, which unveils a complex scenario of dynamical behaviors.

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“…An external forcing can be introduced in light sensitive reactors by periodic changes, see e.g. [SaScWu99,RMMSC03] for a framework and an example.…”

Section: Examplesmentioning

confidence: 99%

Exponential Estimates in Averaging and Homogenisation

Matthies

2006

Analysis, Modeling and Simulation of Multiscale Problems

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Abstract. Many partial differential equations with rapid spatial or temporal scales have effective descriptions which can be derived by homogenisation or averaging. In this article we deal with examples, where quantitative estimates of the error is possible for higher order homogenisation and averaging. In particular, we provide theorems, which allow homogenisation and averaging beyond all orders by giving exponential estimates of appropriately averaged and homogenised descriptions.Methods include iterated averaging transformations, optimal truncation of asymptotic expansions and highly regular solutions (Gevrey regularity). Prototypical examples are reaction-diffusion equations with heterogeneous reaction terms or rapid external forcing, nonlinear Schrödinger equations describing dispersion management, and second-order linear elliptic equations.

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Dynamics of Turing Patterns under Spatiotemporal Forcing

Cited by 86 publications

References 19 publications

Instabilities in spatially extended predator–prey systems: Spatio-temporal patterns in the neighborhood of Turing–Hopf bifurcations

Instabilities in spatially extended predator–prey systems: Spatio-temporal patterns in the neighborhood of Turing–Hopf bifurcations

Traveling-Stripe Forcing Generates Hexagonal Patterns

Exponential Estimates in Averaging and Homogenisation

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