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Self-organized criticality in spatial evolutionary game theory

T Killingback1, M Doebeli

  • 1CERN, CH-1211 Geneva, Switzerland.

Journal of Theoretical Biology
|June 19, 1998
PubMed
Summary
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This study introduces a new class of cellular automata derived from evolutionary game theory. These models exhibit self-organized criticality, displaying complex dynamics and scale-free behavior across time and length scales.

Area of Science:

  • Complex Systems Science
  • Computational Physics
  • Theoretical Computer Science

Background:

  • Self-organized criticality (SOC) is a key concept for explaining scale-free phenomena in nature.
  • Cellular automata (CA) are effective computational models for studying SOC.

Purpose of the Study:

  • To investigate a novel class of CA models based on evolutionary game theory.
  • To explore the conditions under which these CA models exhibit complex dynamics and SOC.

Main Methods:

  • Developed a discrete one-parameter family of cellular automata.
  • Analyzed the system dynamics for a range of parameter values.
  • Investigated statistical measures for power-law behavior.

Main Results:

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  • Identified a parameter range exhibiting complex dynamics and long-range correlations in time and space.
  • Demonstrated the emergence of a self-organized critical state.
  • Observed power-law behavior in statistical measures, indicating scale-invariance.

Conclusions:

  • The proposed CA construction successfully models self-organized criticality.
  • These models offer a framework for understanding emergent scale-free phenomena.
  • The system dynamics evolve towards a critical state with structures across all scales.