Colored-noise-induced multistability in nonequilibrium phase transitions

Kim, Seunghwan; Park, Seon Hee; Ryu, Cheolho

doi:10.1103/physreve.58.7994

Cited by 26 publications

(31 citation statements)

References 15 publications

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“…Interestingly, they showed also that in the presence of temporal correlation disorder is favored for large enough spatial coupling, another counterintuitive effect. Kim et al ͑1998͒, on the other hand, showed that a dichotomous multiplicative noise, acting also on model ͑94͒, rendered the disordering reentrant transition discontinuous, giving rise to bistability at large noise levels between the ordered and disordered phases.…”

Section: ͑1999͒mentioning

confidence: 99%

Spatiotemporal order out of noise

2007

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Natural systems are undeniably subject to random fluctuations, arising from either environmental variability or thermal effects. The consideration of those fluctuations supposes to deal with noisy quantities whose variance might at times be a sizable fraction of their mean levels. It is known that, under these conditions, noisy fluctuations can interact with the system's nonlinearities to render counterintuitive behavior, in which an increase in the noise level produces a more regular behavior. In systems with spatial degrees of freedom, this regularity takes the form of spatiotemporal order. An overview is presented of the mechanisms through which noise induces, enhances, and sustains ordered behavior in passive and active nonlinear media, and different spatiotemporal phenomena are described resulting from these effects. The general theoretical framework used in the analysis of these effects is reviewed, encompassing the theory of stochastic partial differential equations and coupled sets of ordinary stochastic differential equations. Experimental observations of self-organized behavior arising out of noise are also described, and details on the numerical algorithms needed in the computer simulation of these problems are given.

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Section: ͑1999͒mentioning

confidence: 99%

Spatiotemporal order out of noise

2007

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“…(15) by φ ± respectively. The amplitude A(k * ) and the constant B are the mean field quantities that must be chosen self-consistently to complete the solution of the problem.…”

Section: Modulated Mean-field Theorymentioning

confidence: 99%

“…We start with m = 1, a choice that has been made in a number of studies of purely noise induced transitions [13,14,15]. This is a particularly useful example because it can be solved analytically in mean field.…”

Section: Mean Field Solution -Particular Examples and Phase Diagramsmentioning

confidence: 99%

Spatial patterns induced purely by dichotomous disorder

Buceta

Lindenberg

2003

Phys. Rev. E

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“…6,7 The noise-induced first order phase transition was also shown to be possible. [8][9][10] The systems with colored noise were investigated by various groups. [10][11][12] Furthermore, the bistability created by the noise-induced phase transition exhibits stochastic resonance when a time-periodic perturbation is added.…”

Section: Introductionmentioning

confidence: 99%

“…[8][9][10] The systems with colored noise were investigated by various groups. [10][11][12] Furthermore, the bistability created by the noise-induced phase transition exhibits stochastic resonance when a time-periodic perturbation is added. 13 This result suggests that the bistability is stable against external perturbation despite that it is purely generated by noise.…”

Section: Introductionmentioning

confidence: 99%

Macroscopic limit cycle via noise-induced phase transition

2003

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Bistability generated via a noise-induced phase transition is reexamined from the view of macroscopic dynamical systems, which clarifies the role of fluctuation better than the conventional Fokker-Plank or Langevin equation approach. Using this approach, we investigated the spatially-extended systems with two degrees of freedom per site. The model systems undergo a noise-induced phase transition through a Hopf bifurcation, leading to a macroscopic limit cycle motion similar to the deterministic relaxation oscillation.

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Colored-noise-induced multistability in nonequilibrium phase transitions

Cited by 26 publications

References 15 publications

Spatiotemporal order out of noise

Spatiotemporal order out of noise

Spatial patterns induced purely by dichotomous disorder

Macroscopic limit cycle via noise-induced phase transition

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