Stochastic patterns in a 1D Rock–Paper–Scissor model with mutation

Résultats de recherche: Livre/Rapport/RevueAutre rapport

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Résumé

In the framework of a 1D cyclic competition model, the Rock–Paper–Scissor model, where bacteria are allowed to mutate and move in space, we study the formation of stochastic patterns, where all the bacteria species do coexist. We modelled the problem using an individual–based setting and using the system size van Kampen expansion to deal with the Master Equation, we have been able to characterise the spatio–temporal patterns using the power spectrum of the fluctuations. We proved that such patterns are robust against the intrinsic noise and they can be found for parameters values beyond the ones fixed by the deterministic approach. We complement such analytical results with numerical simulations based on the Gillespie’s algorithm.
langue originaleAnglais
EditeurNamur center for complex systems
Nombre de pages23
Volume1
Edition14
étatPublié - 17 janv. 2014

Série de publications

NomnaXys Technical Report Series
EditeurUniversity of Namur
Numéro14
Volume1

Empreinte digitale

mutations
bacteria
trucks
complement
power spectra
expansion
simulation

Citer ceci

Cianci, C., & Carletti, T. (2014). Stochastic patterns in a 1D Rock–Paper–Scissor model with mutation. (14 Ed.) (naXys Technical Report Series; Vol 1, Numéro 14). Namur center for complex systems.
Cianci, Claudia ; Carletti, Timoteo. / Stochastic patterns in a 1D Rock–Paper–Scissor model with mutation. 14 Ed. Namur center for complex systems, 2014. 23 p. (naXys Technical Report Series; 14).
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abstract = "In the framework of a 1D cyclic competition model, the Rock–Paper–Scissor model, where bacteria are allowed to mutate and move in space, we study the formation of stochastic patterns, where all the bacteria species do coexist. We modelled the problem using an individual–based setting and using the system size van Kampen expansion to deal with the Master Equation, we have been able to characterise the spatio–temporal patterns using the power spectrum of the fluctuations. We proved that such patterns are robust against the intrinsic noise and they can be found for parameters values beyond the ones fixed by the deterministic approach. We complement such analytical results with numerical simulations based on the Gillespie’s algorithm.",
keywords = "stochastic processes, nonlinear dynamics, spatio-temporal patterns, stochastic patterns, stochastic simulations",
author = "Claudia Cianci and Timoteo Carletti",
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Cianci, C & Carletti, T 2014, Stochastic patterns in a 1D Rock–Paper–Scissor model with mutation. naXys Technical Report Series, Numéro 14, VOL. 1, VOL. 1, 14 edn, Namur center for complex systems.

Stochastic patterns in a 1D Rock–Paper–Scissor model with mutation. / Cianci, Claudia; Carletti, Timoteo.

14 Ed. Namur center for complex systems, 2014. 23 p. (naXys Technical Report Series; Vol 1, Numéro 14).

Résultats de recherche: Livre/Rapport/RevueAutre rapport

TY - BOOK

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AU - Cianci, Claudia

AU - Carletti, Timoteo

PY - 2014/1/17

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N2 - In the framework of a 1D cyclic competition model, the Rock–Paper–Scissor model, where bacteria are allowed to mutate and move in space, we study the formation of stochastic patterns, where all the bacteria species do coexist. We modelled the problem using an individual–based setting and using the system size van Kampen expansion to deal with the Master Equation, we have been able to characterise the spatio–temporal patterns using the power spectrum of the fluctuations. We proved that such patterns are robust against the intrinsic noise and they can be found for parameters values beyond the ones fixed by the deterministic approach. We complement such analytical results with numerical simulations based on the Gillespie’s algorithm.

AB - In the framework of a 1D cyclic competition model, the Rock–Paper–Scissor model, where bacteria are allowed to mutate and move in space, we study the formation of stochastic patterns, where all the bacteria species do coexist. We modelled the problem using an individual–based setting and using the system size van Kampen expansion to deal with the Master Equation, we have been able to characterise the spatio–temporal patterns using the power spectrum of the fluctuations. We proved that such patterns are robust against the intrinsic noise and they can be found for parameters values beyond the ones fixed by the deterministic approach. We complement such analytical results with numerical simulations based on the Gillespie’s algorithm.

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KW - stochastic simulations

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Cianci C, Carletti T. Stochastic patterns in a 1D Rock–Paper–Scissor model with mutation. 14 Ed. Namur center for complex systems, 2014. 23 p. (naXys Technical Report Series; 14).