Jump of the minimal site and a new correlation function in the Bak-Sneppen model

A new type of spatio-temporal correlation function for the process approaching the self-organized criticality is investigated within the Bak-Sneppen model for biological evolution. In terms of the “directional shorter distance” between the two sites with minimum fitness at two successive updates, the correlation function is defined and studied numerically for the nearest- and random-neighbor versions of the model. Qualitatively different behaviors of the jump of the minimal site in the two models are presented, and the behaviors of the correlation functions are shown also different. Received 14 April 2001 and Received in final form 28 June 2001