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Influence of physical interactions on spatiotemporal patterns.

Chengjie Luo1, David Zwicker1

  • 1Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077 Göttingen, Germany.

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Physical interactions significantly alter spatiotemporal patterns in cyclic dominant reactions, like the rock-paper-scissors game. These interactions modify spiral wave dynamics and can lead to novel patterns such as oscillating lattices or phase separation.

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Area of Science:

  • Complex Systems
  • Theoretical Ecology
  • Chemical Kinetics

Background:

  • Spatiotemporal patterns are commonly modeled using reaction-diffusion equations.
  • These models often neglect physical interactions between constituents, potentially limiting their accuracy.
  • Cyclic dominant reactions, such as the rock-paper-scissors game, are known to produce spiral waves under ideal diffusion.

Purpose of the Study:

  • To investigate the impact of physical interactions on spatiotemporal patterns in cyclic dominant reactions.
  • To generalize reaction-diffusion models by incorporating physical interactions.
  • To understand how these interactions influence pattern formation and dynamics.

Main Methods:

  • Generalized diffusion to include physical interaction effects.
  • Studied cyclic dominant reactions, exemplified by the rock-paper-scissors game.
  • Analyzed pattern formation under varying strengths and types (repulsive/attractive) of physical interactions.

Main Results:

  • Weak interactions altered spiral wave length and time scales, mapping to the complex Ginzburg-Landau equation.
  • Strong repulsive interactions resulted in oscillating lattices.
  • Strong attractive interactions led to phase separation alongside chemical oscillations and spiral wave cores.

Conclusions:

  • Physical interactions are crucial for accurately modeling spatiotemporal patterns in nature.
  • The findings offer insights into pattern formation mechanisms and may explain biodiversity maintenance in ecological systems.