Disordered waves in a homogeneous, motionless excitable medium

Markus, Mario; Kloss, Guy K.; Kusch, Ingo

doi:10.1038/371402a0

Cited by 67 publications

(29 citation statements)

References 21 publications

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“…The travelling and spiral waves here show a similar behaviour to waves in prebiotic evolution 6 , in host-parasitoid systems 7 , as well as in excitable media (see Refs 4,[8][9][10] and references therein) such as chemical reactions, heart muscle and epidemics. In the latter, the black, dashed and white regions shown in Fig 3b, correspond to excited, refractory (or immune) and excitable (or resting) states, respectively.…”

Section: Resulting Modesmentioning

confidence: 69%

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Markus¹,

Schulz²,

Goles³

2002

ScienceAsia

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We present an evolutionary model that marks an encounter of two seemingly unrelated disciplines: population dynamics and number theory. Assuming mutations and selection of predators and prey, we show that prey cycles with non-prime lengths are unstable, while cycles with prime lenghts are stable. Allowing arbitrarily long cycles, this model is a number-theoretical tool for the calculation of large prime numbers. An extension of this purely temporal process to an evolutionary game on a spatial array leads to homogeneity, or to travelling or spiral waves having a predominance of prime prey cycle lengths. These results may be related to the appearance of cicadas (genus Magicicadae) every 13 or 17 years.

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Section: Resulting Modesmentioning

confidence: 69%

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Markus¹,

Schulz²,

Goles³

2002

ScienceAsia

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“…The mechanism of elimination is quite different from what is already known from experiments and numerical simulations: the annihilation of two counterrotating spirals; 8 collision of the spiral with the boundary; 5 the global suppression of wave propagation. It is also different from aperiodic modulation of wave fronts resulting in wave breaks 29 (where there are some mistakes because light intensity of 300 mW/m 2 reported in ref 29 is definitely not enough to induce wave destabilization in the Ru-catalyzed BZ reaction).…”

Section: Discussionmentioning

confidence: 95%

“…Light is known to inhibit the BZ reaction, [18][19][20] and the change of light illumination gives us the possibility to control the system with the only delay, defined by chemical kinetics, known to be no more than a few seconds. 20 The possibility of destabilizing the wave pattern with an increase of light intensity was already shown in ref 29.…”

Section: Introductionmentioning

confidence: 93%

Fast Selective Elimination of Spiral Waves

Agladze¹,

Voignier²,

Hamm³

et al. 1996

J. Phys. Chem.

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Elimination of spiral waves prevents transition to chaotic state in excitable media of different physicochemical nature. In cardiac muscle, to prevent cardiac death, the spiral waves are usually removed together with all propagating waves by a strong electric shock: 5 kV, 20 A ("defibrillation"). We have found an approach to extinguish spiral waves without destroying normally propagating waves. Chemical excitation waves in a spatial open reactor with the Belousov-Zhabotinsky reaction controlled by light were used as an experimental model. We found three different scenarios, depending on the rate of the light change. (i) When the light intensity was increased immediately, the spiral wave was eliminated. (ii) When it was increased slowly enough, the spiral wave survived, increasing its core and diminishing its rotation rate. (iii) When it was increased gradually, at an intermediate rate, the spiral wave survived, but multiple wave breaks appeared at the periphery. Computer modeling has shown that the results obtained are generic and relevant for excitable media of various nature.

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“…Earlier studies focused mainly on simple spiral waves, but these shed little light on the more complex structures in natural spiral patterns such as galaxies, typhoons, seashells, and lichens. Recently, attention has shifted to investigations of complex spiral waves, and four classes of mechanisms responsible for their generation have been identified: ͑1͒ tip meandering, which induces the formation of superspiral structures; 13 ͑2͒ period-doubling bifurcation of the local dynamics, which leads to the formation of line defects on the period-2 n spiral waves; 14,15 ͑3͒ transverse wave instability, which results in the formation of rippling spiral arms 16 or segmentation of spiral segments in the presence of a fast-diffusing inhibitor; 17 ͑4͒ interaction of two steady states, one excitable and the other pseudo-Turing unstable, which also induces the formation of segmented spiral waves. 18 The formation of complex spiral structures usually portends the onset of spiral turbulence, which occurs via spiral breakup.…”

Section: Arm Splitting and Backfiring Of Spiral Waves In Media Displamentioning

confidence: 99%

Arm splitting and backfiring of spiral waves in media displaying local mixed-mode oscillations

Gao

Zhang

Wang

et al. 2009

Chaos: An Interdisciplinary Journal of Nonlinear Science

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The behavior of spiral waves is investigated in a model of reaction-diffusion media supporting local mixed-mode oscillations for a range of values of a control parameter. This local behavior is accompanied by the formation of nodes, at which the arms of the simple spiral waves begin to split. With further parameter changes, this nodal structure loses stability, becoming quite irregular, eventually evolving into turbulence, while the local dynamics increases in complexity. The breakup of the spiral waves arises from a backfiring instability of the nodes induced by the arm splitting. This process of spiral breakup in the presence of mixed-mode oscillations represents an alternative to previously described scenarios of instability of line defects and superspirals in media with period-doubling and quasiperiodic oscillations, respectively.

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Disordered waves in a homogeneous, motionless excitable medium

Cited by 67 publications

References 21 publications

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Fast Selective Elimination of Spiral Waves

Arm splitting and backfiring of spiral waves in media displaying local mixed-mode oscillations

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