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Globally synchronized oscillations in complex cyclic games.

Charlotte Rulquin1, Jeferson J Arenzon2

  • 1École Normale Supérieure, International Center of Fundamental Physics, 45 Rue d'Ulm, 75005 Paris, France and Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, 91501-970 Porto Alegre, Rio Grande do Sul, Brazil.

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This summary is machine-generated.

Introducing long-range interactions into cyclic population models with four species stabilizes global oscillations. This synchronization is surprisingly more efficient in four-species systems than three-species ones, even in heterogeneous environments.

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Area of Science:

  • Theoretical Ecology
  • Complex Systems Dynamics
  • Mathematical Biology

Background:

  • Cyclic population models, like rock-paper-scissors, are established for studying interacting species.
  • Generalizations with S>3 species, especially four species, introduce complex food web structures beyond simple cyclic interactions.
  • Previous work showed distinct three- and four-species phases with localized oscillations on a square lattice.

Purpose of the Study:

  • To investigate the effect of long-range interactions on the stability and synchronization of population dynamics in generalized cyclic models.
  • To determine the conditions under which global oscillations emerge and become stable in systems with more than three species.
  • To compare the synchronization efficiency between three- and four-species coexistence phases.

Main Methods:

  • Utilizing a square lattice model for interacting populations.
  • Introducing a fraction Q of long-range interactions to replace short-range ones.
  • Analyzing population dynamics through the identification of Hopf bifurcations and phase transitions.
  • Investigating the impact of environmental heterogeneity (deviations from χ=0 or 1) on synchronization thresholds.

Main Results:

  • A Hopf bifurcation leads to stable global oscillations when a minimum fraction Q of long-range interactions is introduced.
  • The four-species coexistence phase requires fewer long-range interactions for global synchronization (lower Q) than the three-species phase.
  • Environmental heterogeneity increases the required fraction of long-range interactions (Qc) for synchronization.
  • Increasing Q further can lead to a transition to a single-species absorbing state in the four-species phase, while the three-species phase remains stable.

Conclusions:

  • Global oscillations can be stabilized in generalized cyclic population models (S>3) by introducing long-range interactions.
  • The four-species model exhibits a more efficient synchronization mechanism compared to the three-species model.
  • Synchronization becomes more challenging in heterogeneous environments, suggesting implications for real-world food webs.
  • Global oscillations may be a general characteristic of large, complex food webs with multiple interaction pathways.