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This study reveals two critical states in a 1D cellular automaton, exhibiting power-law avalanche scaling. The system transitions between these states, modeling earthquake supercycles.

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Area of Science:

  • Complex systems
  • Statistical physics
  • Computational modeling

Background:

  • Self-organized criticality (SOC) describes systems that naturally evolve to a critical state.
  • Power-law scaling is a hallmark of critical phenomena, indicating scale-invariant behavior.
  • Cellular automata provide simplified models for complex emergent behaviors.

Purpose of the Study:

  • To investigate the stationary states of a 1D cellular automaton exhibiting power-law avalanche scaling.
  • To analyze the characteristics of the identified fixed points (spiral saddle and saddle with index 1).
  • To demonstrate state migration between self-organized criticality states in a slowly driven system.

Main Methods:

  • Utilized a simple 1D cellular automaton model.
  • Performed computer simulations to observe system evolution.
  • Analyzed statistical properties, focusing on avalanche power-law scaling.
  • Investigated fixed point features and state transitions.

Main Results:

  • Identified two statistically stationary states characterized by power-law scaling of avalanches.
  • Characterized the spiral saddle and saddle with index 1 fixed points.
  • Observed and demonstrated the migration of automaton states between these two SOC states during simulations.
  • Confirmed the system's behavior as a slowly driven process.

Conclusions:

  • The 1D cellular automaton effectively models self-organized criticality with distinct stationary states.
  • The observed state migration provides insights into the dynamics of complex systems.
  • This automaton serves as a valuable toy model for understanding earthquake supercycle phenomena.