The avalanche dynamics in random nearest neighbor models of evolution with interaction strength (Q2495292)

A generalized Bak-Sneppen model (BS model) of biological evolution with interaction strength \(\theta\) is introduced in \(d\)-dimensional space, where the ``nearest neighbors'' are chosen among the \(2d\) neighbors of the extremal site, with the probabilities related to the sizes of the fitnesses. Simulations of one- and two-dimensional models are given. For given \(\theta > 0\), the model can self-organize to a critical state, and the critical threshold \(f_c (\theta)\) decreases as \(\theta\) increases. The exact gap equation depending on \(\theta\) is presented, which reduces to the gap equation of BS model as \(\theta\) tends to infinity. An exact equation for the critical exponent \(\gamma(\theta)\) is also obtained. Scaling relations are established among the six critical exponents of the avalanches of the model.