A model of evolution with interaction strength

TL;DR

This paper introduces a new evolutionary model incorporating interaction strength, demonstrating that the system self-organizes to a critical state with properties dependent on the interaction parameter.

Contribution

It extends the Bak-Sneppen model by including a tunable interaction strength, revealing its effects on critical thresholds and exponents in self-organized criticality.

Findings

Self-organized threshold decreases as interaction strength increases.

Critical exponents depend on interaction strength.

Model maintains some exact equations from Bak-Sneppen model.

Abstract

Interaction strength is introduced in a model of evolution in d-dimension space. It is realized by imposing a constraint concerning 2d differences of fitnesses between that of any extremal site and those of its 2d nearest neighbours at each time step in the evolution of the model. For any given interaction strength between 0 and 1 the model can self-organize to a critical state. Two exact equations found in Bak-Sneppen model still hold in our model for different interaction strength. Simulations of one- and two-dimensional models for ten different values of interaction are given. It is found that self-organized threshold decreases with interaction strength increasing. It is also shown that the critical exponent, and two basic exponents, avalanche distribution, and avalanche dimension, are interaction strength dependent.