Short-ranged memory model with preferential growth

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.