Front dynamics in an oscillatory bistable Belousov-Zhabotinsky chemical reaction

Marts, Bradley; Martinez, Karl; Lin, Anna L.

doi:10.1103/physreve.70.056223

Cited by 21 publications

(15 citation statements)

References 25 publications

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“…1(d)]. This mechanism for the formation of LS has been largely studied (see, for instance, [34][35][36][37][38]), and commonly observed in different physical systems [11][12][13][14][15][16].…”

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confidence: 99%

“…While the interaction between Ising fronts has been widely studied in the literature, leading to the formation of localized structures (LS) or dissipative solitons in a wide range of complex systems [11][12][13][14][15][16], only specific cases concerning the interaction of Bloch walls have been considered [17][18][19][20][21]. In this Letter we show that the interaction of Bloch walls can be very generally described in terms of only two coupled modes of the front, the neutral (or Goldstone) mode and the chiral mode that become unstable at the IB transition.…”

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confidence: 99%

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Theory for the Spatiotemporal Dynamics of Domain Walls close to a Nonequilibrium Ising-Bloch Transition

2015

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We derive a generic model for the interaction of domain walls close to a nonequilibrium-Bloch transition. The universal scenario predicted by the model includes stationary Ising and Bloch localized structures (dissipative solitons), as well as drifting and oscillating Bloch structures. Our theory also explains the behavior of Bloch walls during a collision. The results are confirmed by numerical simulations of the Ginzburg-Landau equation forced at twice its natural frequency and are in agreement with previous observations in several physical systems.

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confidence: 99%

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confidence: 99%

Theory for the Spatiotemporal Dynamics of Domain Walls close to a Nonequilibrium Ising-Bloch Transition

2015

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“…Thus, it could explain experimental observations of transient localized spots in a more general setting. Systems with bistable homogeneous states in which this mechanism could be observed include, for instance, optical systems [21], chemical reactions [22], or vegetation growth models [23].…”

Section: Where We Have Considered That the Evolution Of D(t) Is Much mentioning

confidence: 99%

Front interaction induces excitable behavior

et al. 2017

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Spatially extended systems can support local transient excitations in which just a part of the system is excited. The mechanisms reported so far are local excitability and excitation of a localized structure. Here we introduce an alternative mechanism based on the coexistence of two homogeneous stable states and spatial coupling. We show the existence of a threshold for perturbations of the homogeneous state. Subthreshold perturbations decay exponentially. Superthreshold perturbations induce the emergence of a long-lived structure formed by two back to back fronts that join the two homogeneous states. While in typical excitability the trajectory follows the remnants of a limit cycle, here reinjection is provided by front interaction, such that fronts slowly approach each other until eventually annihilating. This front-mediated mechanism shows that extended systems with no oscillatory regimes can display excitability.

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“…Another typical resonant behavior in this parameter regime is the appearance of localized spot-like structures close to the transverse instability threshold. 31,32 As the NIB bifurcation is approached the dynamics change; instead of fingering and tip splitting; growing transverse perturbations now induce vortex nucleation followed by a nonresonant state of Bloch-front turbulence as Figs. 6 and 7 show.…”

Section: B Bloch-front Turbulencementioning

confidence: 99%

Resonant and nonresonant patterns in forced oscillators

Marts

Hagberg

Meron

et al. 2006

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Uniform oscillations in spatially extended systems resonate with temporal periodic forcing within the Arnold tongues of single forced oscillators. The Arnold tongues are wedge-like domains in the parameter space spanned by the forcing amplitude and frequency, within which the oscillator's frequency is locked to a fraction of the forcing frequency. Spatial patterning can modify these domains. We describe here two pattern formation mechanisms affecting frequency locking at half the forcing frequency. The mechanisms are associated with phase-front instabilities and a Turing-like instability of the rest state. Our studies combine experiments on the ruthenium catalyzed light-sensitive Belousov-Zhabotinsky reaction forced by periodic illumination, and numerical and analytical studies of two model systems, the FitzHugh-Nagumo model and the complex Ginzburg-Landau equation, with additional terms describing periodic forcing.

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Front dynamics in an oscillatory bistable Belousov-Zhabotinsky chemical reaction

Cited by 21 publications

References 25 publications

Theory for the Spatiotemporal Dynamics of Domain Walls close to a Nonequilibrium Ising-Bloch Transition

Theory for the Spatiotemporal Dynamics of Domain Walls close to a Nonequilibrium Ising-Bloch Transition

Front interaction induces excitable behavior

Resonant and nonresonant patterns in forced oscillators

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