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Abstract: We considered a stochastic version of the Bak-Sneppen model SBSM ofecological evolution where the the number $M$ of sites mutated in a mutationevent is restricted to only two. Here the mutation zone consists of only onesite and this site is randomly selected from the neighboring sites at everymutation event in an annealed fashion. The critical behavior of the SBSM isfound to be the same as the BS model in dimensions $d$ =1 and 2. However on thescale-free graphs the critical fitness value is non-zero even in thethermodynamic limit but the critical behavior is mean-field like. Finally $$has been made even smaller than two by probabilistically updating the mutationzone which also shows the original BS model behavior. We conjecture that a SBSMon any arbitrary graph with any small branching factor greater than unity willlead to a self-organized critical state.



Author: S. S. Manna

Source: https://arxiv.org/



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