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

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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.
Original languageEnglish
Pages (from-to)66-78
JournalPhysica A: Statistical Mechanics and its Applications
Volume410
DOIs
Publication statusPublished - 15 Sep 2014

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mutations
Bacteria
Mutation
Competition Model
bacteria
Spatio-temporal Patterns
Master Equation
Power Spectrum
Complement
Fluctuations
trucks
Numerical Simulation
complement
power spectra
Model
expansion
simulation
Framework

Keywords

  • stochastic processes
  • nonlinear dynamics
  • spatio-temporal patterns
  • stochastic patterns
  • stochastic simulations

Cite this

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title = "Stochastic patterns in a 1D Rock–Paper–Scissor model with mutation",
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",
year = "2014",
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AU - Cianci, Claudia

AU - Carletti, Timoteo

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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.

KW - stochastic processes

KW - nonlinear dynamics

KW - spatio-temporal patterns

KW - stochastic patterns

KW - stochastic simulations

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JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

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