Spatial patterns induced purely by dichotomous disorder

Buceta, Javier; Lindenberg, Katja

doi:10.1103/physreve.68.011103

Cited by 19 publications

(15 citation statements)

References 19 publications

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“…However, there are no known exact methods for the integration of . Thus, the analytical evidence for the existence of a noise‐induced transition comes from an approximated approach based on the mean field (Weiss) approximation [ van den Broeck et al , 1994, 1997; Buceta and Lindenberg , 2003]. These approximated analytical results have been supported by numerical simulations [ van den Broeck et al , 1994, 1997; Buceta and Lindenberg , 2003; Porporato and D'Odorico , 2004].…”

Section: Mechanisms Of Pattern Formationmentioning

confidence: 98%

Mathematical models of vegetation pattern formation in ecohydrology

Borgogno¹,

D’Odorico²,

Laio³

et al. 2009

Reviews of Geophysics

289

299

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Highly organized vegetation patterns can be found in a number of landscapes around the world. In recent years, several authors have investigated the processes underlying vegetation pattern formation. Patterns that are induced neither by heterogeneity in soil properties nor by the local topography are generally explained as the result of spatial self‐organization resulting from “symmetry‐breaking instability” in nonlinear systems. In this case, the spatial dynamics are able to destabilize the homogeneous state of the system, leading to the emergence of stable heterogeneous configurations. Both deterministic and stochastic mechanisms may explain the self‐organized vegetation patterns observed in nature. After an extensive analysis of deterministic theories, we review noise‐induced mechanisms of pattern formation and provide some examples of applications relevant to the environmental sciences.

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Section: Mechanisms Of Pattern Formationmentioning

confidence: 98%

Mathematical models of vegetation pattern formation in ecohydrology

Borgogno¹,

D’Odorico²,

Laio³

et al. 2009

Reviews of Geophysics

289

299

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“…However, as in the case of noise, some recent studies lead to the conclusion that diversity might have a constructive role. Some previous work has shown the existence the phase transitions [15] and patterns [16] induced by quenched dichotomous noise. In this paper we will briefly comment on two recently found effects: resonance to an external forcing and common firing, both induced by diversity.…”

Section: Introductionmentioning

confidence: 99%

Collective effects induced by diversity in extended systems

Toral

Tessone

Lopes

2007

Eur. Phys. J. Spec. Top.

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We show that diversity, in the form of quenched noise, can have a constructive effect in the dynamics of extended systems. We first consider a bistable φ 4 model composed by many coupled units and show that the global response to an external periodic forcing is enhanced under the presence of the right amount of diversity (measured as the dispersion in one of the parameters defining the model). As a second example, we consider a system of active-rotators and show that while they are at rest in the homogeneous case, the disorder introduced by the diversity suffices to trigger the appearance of common firings or pulses. Both effects require very simple ingredients and we expect the results presented here to be of interest in similar models.

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“…Dichotomous noise driven phenomena include robust phase synchronization, 22,23 stochastic hypersensitivity, 24,25 enhanced stochastic resonance, 26 hysteresis, 27 and patterning. 28,29 Brute force simulation of the full master equation for genetic networks has already yielded many insights. 30,31 Nevertheless, in practice the sheer number of cellular components often renders such an explicit approach overwhelming.…”

Section: Introductionmentioning

confidence: 99%

Dichotomous noise models of gene switches

Potoyan

Wolynes

2015

The Journal of Chemical Physics

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Molecular noise in gene regulatory networks has two intrinsic components, one part being due to fluctuations caused by the birth and death of protein or mRNA molecules which are often present in small numbers and the other part arising from gene state switching, a single molecule event. Stochastic dynamics of gene regulatory circuits appears to be largely responsible for bifurcations into a set of multi-attractor states that encode different cell phenotypes. The interplay of dichotomous single molecule gene noise with the nonlinear architecture of genetic networks generates rich and complex phenomena. In this paper, we elaborate on an approximate framework that leads to simple hybrid multi-scale schemes well suited for the quantitative exploration of the steady state properties of large-scale cellular genetic circuits. Through a path sum based analysis of trajectory statistics, we elucidate the connection of these hybrid schemes to the underlying master equation and provide a rigorous justification for using dichotomous noise based models to study genetic networks. Numerical simulations of circuit models reveal that the contribution of the genetic noise of single molecule origin to the total noise is significant for a wide range of kinetic regimes. C 2015 AIP Publishing LLC. [http://dx

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Spatial patterns induced purely by dichotomous disorder

Cited by 19 publications

References 19 publications

Mathematical models of vegetation pattern formation in ecohydrology

Mathematical models of vegetation pattern formation in ecohydrology

Collective effects induced by diversity in extended systems

Dichotomous noise models of gene switches

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