Finite systems of deterministic ordinary nonlinear differential equations may be designed to represent forced dissipative hydrodynamic flow. Solutions of these equations can be identified with trajectories in phase space. For those systems with bounded solutions, it is found that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states. Systems with bounded solutions are shown to possess bounded numerical solutions.A simple system representing cellular convection is solved numerically. All (...) of the solutions are found to be unstable, and almost all of them are nonperiodic.The feasibility of very-long-range weather prediction is examined in the light of these results. (shrink)

This article discusses my book, Origins of Order: Self Organization and Selection in Evolution, in the context of the emerging sciences of complexity. Origins, due out of Oxford University Press in early 1992, attempts to lay out a broadened theory of evolution based on the marriage of unexpected and powerful properties of self organization which arises in complex systems, properties which may underlie the origin of life itself and the emergence of order in ontogeny, and the continuing action of natural (...) selection. The three major themes are: 1) that such self organized properties lie to hand for selection's further molding; 2) hence that the order we see is not due to selection alone, but in part reflects the order selection has always acted upon; 3) and finally that the marriage of natural order and natural selection may inevitably lead living entitites to a novel organized state, lying on the edge between order and chaos, as the inevitable evolutionary attractor of selection for the capacity to adapt. (shrink)

Recent observations of power-law distributions in the connectivity of complex networks came as a big surprise to researchers steeped in the tradition of random networks. Even more surprising was the discovery that power-law distributions also characterize many biological and social networks. Many attributed a deep significance to this fact, inferring a “universal architecture” of complex systems. Closer examination, however, challenges the assumptions that (1) such distributions are special and (2) they signify a common architecture, independent of the system's specifics. The (...) real surprise, if any, is that power-law distributions are easy to generate, and by a variety of mechanisms. The architecture that results is not universal, but particular; it is determined by the actual constraints on the system in question. BioEssays 27:1060–1068, 2005. © 2005 Wiley Periodicals, Inc. (shrink)