Spatial Resonances and Superposition Patterns in a Reaction-Diffusion Model with Interacting Turing Modes

Yang, Lingfa; Dolnik, Miloš; Zhabotinsky, Anatol M.; Epstein, Irving R.

doi:10.1103/physrevlett.88.208303

Cited by 125 publications

(92 citation statements)

References 19 publications

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“…Moreover, in [69,70] a variety of both stationary and oscillating structures were obtained in the numerical simulations of a system with interacting modes. On the other hand, due to the interaction between Turing and Hopf instabilities, oscillatory Turing patterns were also found in the Belousov-Zhabotinsky reaction in a water-in-oil microemulsion [34] and in the chlorine dioxide-iodine-malonic acid (CDIMA) reaction [50].…”

Section: Introductionmentioning

confidence: 99%

Spatio-temporal organization in a morphochemical electrodeposition model: Hopf and Turing instabilities and their interplay

2014

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In this paper, we investigate from a theoretical point of view the 2D reaction-diffusion system for electrodeposition coupling morphology and surface chemistry, presented and experimentally validated in Bozzini et al. (2013 J. Solid State Electr. 17, 467-479). We analyse the mechanisms responsible for spatio-temporal organization. As a first step, spatially uniform dynamics is discussed and the occurrence of a supercritical Hopf bifurcation for the local kinetics is proved. In the spatial case, initiation of morphological patterns induced by diffusion is shown to occur in a suitable region of the parameter space. The intriguing interplay between Hopf and Turing instability is also considered, by investigating the spatio-temporal behaviour of the system in the neighbourhood of the codimensiontwo Turing-Hopf bifurcation point. An ADI (Alternating Direction Implicit) scheme based on high-order finite differences in space is applied to obtain numerical approximations of Turing patterns at the steady state and for the simulation of the oscillating Turing-Hopf dynamics.

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Section: Introductionmentioning

confidence: 99%

Spatio-temporal organization in a morphochemical electrodeposition model: Hopf and Turing instabilities and their interplay

2014

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“…12), 14 (Yang and Epstein, 2003a). Interaction between a pair of Turing instabilities can occur in bistable and in multilayer systems and is thought to be responsible for "black eye" and "white eye" superlattice patterns (Bachir et al, 2001;Yang et al, 2002).…”

Section: Patterns Involving Interacting Instabilitiesmentioning

confidence: 99%

Pattern formation mechanisms in reaction-diffusion systems

Vanag¹,

Epstein²

2009

Int. J. Dev. Biol.

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In systems undergoing chemical reaction and diffusion, a remarkable variety of spatially structured patterns, stationary or moving, local or global, can arise, many of them reminiscent of forms and phenomena seen in living systems. Chemical systems offer the advantage that one can often control the parameters that determine the patterns formed and can thereby probe fundamental issues about pattern formation, with possible insights into biologically relevant phenomena. We present experimental examples and discuss several mechanisms by which such spatiotemporal structure may arise, classifying the mechanisms according to the type of instability that results in pattern formation. In some systems, the pattern that emerges depends not only on the chemical and physical parameters but also on the initial state of the system. Interactions between instabilities can result in particularly complex patterns.

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“…Interest in reaction-diffusion systems composed of spatially interacting layers has increased over the past years [6][7][8][9]. Nonlinear pattern formation systems have been successfully coupled numerically and experimentally in a variety of systems, such as the well-known CDIMA (chorine dioxideiodine-malonic acid) reaction [10,11].…”

Section: Introductionmentioning

confidence: 99%

Interaction of chemical patterns in coupled layers

et al. 2011

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We investigate the interaction between reaction-diffusion systems coupled by diffusion. The photosensitive CDIMA (chorine dioxide-iodine-malonic acid) reaction allows us to study experimentally the mutual influence of two layers of Turing patterns coupled via a diffusive interaction. By illuminating each of the layers with different intensities of homogeneous external light, the chemical conditions in each layer can be shifted, allowing us to study the result of diffusive interaction between Turing patterns with different spatial configurations. Our experiments suggest a complex scenario for the interaction between different patterns, strongly dependent on the spatial characteristics of the interacting patterns. Numerical simulations are also reported in full agreement with experimental observations.

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Spatial Resonances and Superposition Patterns in a Reaction-Diffusion Model with Interacting Turing Modes

Cited by 125 publications

References 19 publications

Spatio-temporal organization in a morphochemical electrodeposition model: Hopf and Turing instabilities and their interplay

Spatio-temporal organization in a morphochemical electrodeposition model: Hopf and Turing instabilities and their interplay

Pattern formation mechanisms in reaction-diffusion systems

Interaction of chemical patterns in coupled layers

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