Spatio-temporal chaos in closed and open systems (Q1336513)

Temporal chaos coupled with spatial variability is generic to turbulent phenomena and is associated with spatial pattern formation. The paper gives a review of such spatio-temporal chaos with a number of references (here 99), among which further reviews with extensive bibliography, in reference to special topics, can be found. The definition of spatio- temporal chaos is by no means clear and unambiguously accepted, and little basic understanding has been developed of phenomena complex in both space and time. The stage of exploration is rather phenomenological at the moment, and one seeks for methods allowing to recognize and qualify temporal chaos beyond the purely temporal venue. The paper begins with discussing chaos in temporal systems. Next the authors consider purely spatial, static chaos, finally passing to an example of spatio-temporal complexity, i.e. turbulent fluid flow. Much space is devoted to the spatio-temporal chaos in coupled map lattices: dynamical systems with discrete time (map), discrete space (lattice), and a continuous state. The concluding section summarizes quantifiers for spatio-temporal chaos, most frequent in the literature.