Abstract
A generalized Bak-Sneppen model (BS model) of biological evolution with interaction strength θ is introduced in d-dimensional space, where the “nearest neighbors” are chosen among the 2 d 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 θ > 0, the model can self-organize to a critical state, and the critical threshold f c ( θ) decreases as θ increases. The exact gap equation depending on θ is presented, which reduces to the gap equation of BS model as θ tends to infinity. An exact equation for the critical exponent γ( θ) is also obtained. Scaling relations are established among the six critical exponents of the avalanches of the model.
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