On the emergence of complex systems on the basis of the coordination of complex behaviors of their elements

We argue that the coordination of the activities of individual complex agents enables a system to develop and sustain complexity at a higher level. We exemplify relevant mechanisms through computer simulations of a toy system, a coupled map lattice with transmission delays. The coordination here is achieved through the synchronization of the chaotic operations of the individual elements, and on the basis of this, regular behavior at a longer temporal scale emerges that is inaccessible to the uncoupled individual dynamics. The purpose of this article is to challenge the view, often expressed and perhaps prevalent in most discussions, that the essence of complex systems lies in the emergence of complex structures from the non-linear interaction of many simple elements that obey simple rules. Typically, these rules consist only of 0-1 alternatives selected in response to the input received, as in many prototypes like cellular automata, Boolean networks, spin systems, etc. We do not intend to deny that quite intricate patterns and structures can occur in such systems. However, these are toy systems, and the systems occurring in reality rather consist of elements that individually are quite complex themselves. This brings Max Planck Institute for Mathematics in the Sciences, Inselstr.22-26, 04103 Leipzig, Germany, {fatay, jost}@mis.mpg.de Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA, [email protected] Throughout this essay, we employ the term “complex” only in some vague and metaphorical manner, without any attempt at quantifying it. This should not obscure the general thesis presented here.