On the physical relevance of extremal dynamics
Department of Mathematics, Imperial College - 180 Queens Gate
London SW7 2BZ, UK
2 Blackett Laboratory, Imperial College - Prince Consort Road London SW7 2BZ, UK
Accepted: 9 February 2000
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.
PACS: 05.65+b – Self-organised systems / 05.45-a – Nonlinear dynamics and nonlinear dynamical systems / 87.10+e – General theory and mathematical aspects
© EDP Sciences, 2000