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The HoneyComb Paradigm for Research on Collective Human Behavior
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Published on: January 19, 2019

Junctions and spiral patterns in generalized rock-paper-scissors models.

P P Avelino1, D Bazeia, L Losano

  • 1Centro de Astrofísica da Universidade do Porto, Rua das Estrelas, 4150-762 Porto, Portugal.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 4, 2012
PubMed
Summary
This summary is machine-generated.

We studied generalized rock-paper-scissors models with many species. Our findings show N-armed spiral patterns can emerge, offering new insights into ecological complexity and population dynamics.

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Area of Science:

  • Ecology
  • Mathematical Biology
  • Theoretical Ecology

Background:

  • Rock-paper-scissors models are fundamental for studying species coexistence.
  • Previous research primarily focused on models with a limited number of species.
  • Understanding complex population dynamics in multi-species systems remains a challenge.

Purpose of the Study:

  • To investigate population dynamics in generalized rock-paper-scissors models with an arbitrary number of species (N).
  • To analyze the emergence of spatial patterns, specifically spiral patterns, in these generalized models.
  • To determine the scaling laws associated with pattern formation and interface networks.

Main Methods:

  • Development and analysis of generalized rock-paper-scissors models with N species.
  • Modification of bidirectional predation to include N-cyclic predator-prey rules.
  • Mathematical analysis of interface networks, junction types, and pattern scaling laws.

Main Results:

  • Spiral patterns with N arms can emerge for both odd and even N.
  • An interface network with Y-type junctions follows the scaling law L∝t1/2.
  • N-armed spiral patterns can form with a constant characteristic length scale.

Conclusions:

  • Generalized rock-paper-scissors models can exhibit complex spatial structures like N-armed spirals.
  • The study establishes a clear link between interface junctions and spiral pattern formation.
  • These findings extend previous work and have implications for understanding biological complexity in diverse ecosystems.