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
PublisherNamur center for complex systems
Number of pages23
Volume1
Edition14
Publication statusPublished - 17 Jan 2014

Publication series

NamenaXys Technical Report Series
PublisherUniversity of Namur
No.14
Volume1

Fingerprint

mutations
bacteria
trucks
complement
power spectra
expansion
simulation

Keywords

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

Cite this

Cianci, C., & Carletti, T. (2014). Stochastic patterns in a 1D Rock–Paper–Scissor model with mutation. (14 ed.) (naXys Technical Report Series; Vol. 1, No. 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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Cianci, C & Carletti, T 2014, Stochastic patterns in a 1D Rock–Paper–Scissor model with mutation. naXys Technical Report Series, no. 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, No. 14).

Research output: Book/Report/JournalOther report

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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.

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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).