Heterogeneous Sources of Target Patterns in Reaction−Diffusion Systems

Bugrim, Andrej; Dolnik, Miloš; Zhabotinsky, and Anatol M.; Epstein, Irving R.

doi:10.1021/jp961603t

Cited by 26 publications

(22 citation statements)

References 30 publications

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“…This finding is consistent with the observations of a variety of excitable systems (1,3,16). We point out, however, that a strongly localized heterogeneity will have a similar effect, so our finding is not inconsistent with the observations of the Belousov-Zhabotinsky reaction (1,20,31).…”

supporting

confidence: 92%

Noise can play an organizing role for the recurrent dynamics in excitable media

Muratov

Vanden‐Eijnden

Weinan

2007

Proc. Natl. Acad. Sci. U.S.A.

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We analyze patterns of recurrent activity in a prototypical model of an excitable medium in the presence of noise. Without noise, this model robustly predicts the existence of spiral waves as the only recurrent patterns in two dimensions. With small noise, however, we found that this model is also capable of generating coherent target patterns, another type of recurrent activity that is widely observed experimentally. These patterns remain essentially deterministic despite the presence of the noise, yet their existence is impossible without it. Their degree of coherence can also be made arbitrarily high for wide ranges of the parameters, which does not require fine-tuning. Our findings demonstrate the need to reexamine current modeling approaches to active biological media.stochastic resonance ͉ noise-induced coherence ͉ target patterns

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supporting

confidence: 92%

Noise can play an organizing role for the recurrent dynamics in excitable media

Muratov

Vanden‐Eijnden

Weinan

2007

Proc. Natl. Acad. Sci. U.S.A.

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“…The width does not show any significant change with time but it is confirmed to slightly decrease as [Hg 2+ ] 0 increases. This fact shares similarity with the BZ reaction in the experimental and theoretical work conducted by Bugrim et al 39 …”

Section: Physical Chemistry Chemical Physics Accepted Manuscriptsupporting

confidence: 86%

Targets, ripples and spirals in a precipitation system with anomalous dispersion

Ayass

Lagzi

Al-Ghoul

2015

Phys. Chem. Chem. Phys.

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We present a novel reaction-diffusion system that exhibits three-dimensional superdiffusive traveling waves without utilizing any external forces. These waves include single circular targets, spirals, and ripples as well as phase-like waves. The system is based on the interplay of the precipitation reaction of mercuric iodide in a gel medium, its polymorphic transformation to a different crystalline form, and its redissolution in excess iodide. A phase diagram is constructed as a function of the initial concentrations of the reagents. The spatiotemporal evolution of these waves is thoroughly analyzed and seems to be a consequence of an anomalous dispersion relationship. Pattern selection and wavelengths of propagating waves are found to depend on initial concentrations of the reactants. The breakup of the waves is also investigated. While the breakdown of ripples and spirals is shown to be a consequence of a Doppler-like instability in conjunction with anomalous dispersion, the targets undergo a boundary defect-mediated breakup.

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“…As proved by previous experiments [14][15][16] as well as numerical simulations of inhomogeneous CGLE [17], the existence of target waves is attributed to local inhomogeneities which play the role of pacemakers, changing the local frequency of the bulk oscillation ͑ 0 ͒ [18]. As a result, a target wave with the same frequency as the pacemaker ͑ T ͒ is generated.…”

Section: Discussionmentioning

confidence: 75%

Spatiotemporal chaos control with a target wave in the complex Ginzburg-Landau equation system

et al. 2004

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An effective method for controlling spiral turbulence in spatially extended systems is realized by introducing a spatially localized inhomogeneity into a two-dimensional system described by the complex Ginzburg-Landau equation. Our numerical simulations show that with the introduction of the inhomogeneity, a target wave can be produced, which will sweep all spiral defects out of the boundary of the system. The effects exist in certain parameter regions where the spiral waves are absolutely unstable. A theoretical explanation is given to reveal the underlying mechanism.

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Heterogeneous Sources of Target Patterns in Reaction−Diffusion Systems

Cited by 26 publications

References 30 publications

Noise can play an organizing role for the recurrent dynamics in excitable media

Noise can play an organizing role for the recurrent dynamics in excitable media

Targets, ripples and spirals in a precipitation system with anomalous dispersion

Spatiotemporal chaos control with a target wave in the complex Ginzburg-Landau equation system

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