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Short-ranged memory model with preferential growth.

Ana L Schaigorodsky1, Juan I Perotti1, Nahuel Almeira1

  • 1Instituto de Física Enrique Gaviola (IFEG-CONICET), Ciudad Universitaria, 5000 Córdoba, Argentina and Facultad de Matemática, Astronomía, Física y Computación, Universidad Nacional de Córdoba, 5000 Córdoba, Argentina.

Physical Review. E
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Summary
This summary is machine-generated.

This study introduces a bounded memory Yule-Simon model for preferential growth. The model explains power-law distributions and bursty dynamics observed in complex systems by balancing innovation and oblivion rates.

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Area of Science:

  • Complex Systems Science
  • Statistical Physics
  • Network Science

Background:

  • Preferential growth models, like the Yule-Simon model, are fundamental in understanding how systems evolve over time.
  • Bounded memory effects are crucial in many real-world phenomena but are often overlooked in standard models.

Purpose of the Study:

  • To introduce and analyze a modified Yule-Simon model incorporating a finite kernel to represent bounded memory.
  • To investigate the resulting lifetime and popularity distributions and their emergent properties.

Main Methods:

  • Analytical arguments combined with extensive numerical simulations.
  • Mapping model dynamics to Markov chains for lifetime distribution analysis.
  • Mapping model dynamics to branching processes for popularity distribution analysis.

Main Results:

  • The model generates power-law distributions for lifetime and popularity, consistent with empirical ecological data.
  • Varying the innovation rate reveals characteristics of a continuous phase transition.
  • Near the critical point, time series exhibit power-law distributions and bursty dynamics, similar to solar flare activity.

Conclusions:

  • A bounded memory Yule-Simon model provides a framework for understanding complex system properties.
  • Balancing innovation and oblivion rates is key to explaining observed phenomena like power laws and bursty dynamics.