Self-organized criticality and punctuated equilibria

Many natural phenomena evolve intermittently, with periods of tranquillity interrupted by bursts of activity, rather than following a smooth gradual path. Examples include earthquakes, volcanic eruptions, solar flares, gamma-ray bursts, and biological evolution. Stephen Jay Gould and Niles Eldredge have coined the term ''punctuated equilibria' for this behavior. We argue that punctuated equilibria reflects the tendency of dynamical systems to evolve towards a critical state, and review recent work on simple models. A good metaphoric picture is one where the systems are temporarily trapped in valleys of deformable, interacting landscapes. Similarities with spin glasses are pointed out. Punctuated equilibria are essential for the emergence of complex phenomena. The periods of stasis allow the system to remember its past history; yet the intermittent events permit further change.