On the physical relevance of extremal dynamics

PACS. 05.65+b – Self-organised systems. PACS. 05.45-a – Nonlinear dynamics and nonlinear dynamical systems. PACS. 87.10+e – General theory and mathematical aspects. Abstract. – Taking the Bak-Sneppen evolution model as an example (Phys. Rev. Lett., 71 (1993) 4083), we study extremal dynamics where M> 1 smallest barriers are simultaneously updated as opposed to models in the limit where only the smallest barrier is updated. We investigate the scaling properties of the nearest-neighbour and the random-neighbour model. We demonstrate that the behaviour of models with extremal dynamics in the limit of single update per time step is irrelevant to physical observations. Introduction. – Extremal dynamics is used to model the temporal evolution of many different systems. Invasion percolation is one of the most prominent examples [1] but attempts have been also made to catch some of the salient features of biological evolution in models involving extremal dynamics [2, 3] as well as in some other models related to self-organised criticality [4, 5]. In extremal models, the dynamics consist of a global search for the site i