The field of chaotic synchronization has grown considerably since its advent in 1990. Several subdisciplines and "cottage industries" have emerged that have taken on bona fide lives of their own. Our purpose in this paper is to collect results from these various areas in a review article format with a tutorial emphasis. Fundamentals of chaotic synchronization are reviewed first with emphases on the geometry of synchronization and stability criteria. Several widely used coupling configurations are examined and, when available, experimental demonstrations of their success (generally with chaotic circuit systems) are described. Particular focus is given to the recent notion of synchronous substitution-a method to synchronize chaotic systems using a larger class of scalar chaotic coupling signals than previously thought possible. Connections between this technique and well-known control theory results are also outlined. Extensions of the technique are presented that allow so-called hyperchaotic systems (systems with more than one positive Lyapunov exponent) to be synchronized. Several proposals for "secure" communication schemes have been advanced; major ones are reviewed and their strengths and weaknesses are touched upon. Arrays of coupled chaotic systems have received a great deal of attention lately and have spawned a host of interesting and, in some cases, counterintuitive phenomena including bursting above synchronization thresholds, destabilizing transitions as coupling increases (short-wavelength bifurcations), and riddled basins. In addition, a general mathematical framework for analyzing the stability of arrays with arbitrary coupling configurations is outlined. Finally, the topic of generalized synchronization is discussed, along with data analysis techniques that can be used to decide whether two systems satisfy the mathematical requirements of generalized synchronization. (c) 1997 American Institute of Physics.

SignificanceDecades of research have fostered the now-prevalent assumption that noncrop habitat facilitates better pest suppression by providing shelter and food resources to the predators and parasitoids of crop pests. Based on our analysis of the largest pest-control database of its kind, noncrop habitat surrounding farm fields does affect multiple dimensions of pest control, but the actual responses of pests and enemies are highly variable across geographies and cropping systems. Because noncrop habitat often does not enhance biological control, more information about local farming contexts is needed before habitat conservation can be recommended as a viable pest-suppression strategy. Consequently, when pest control does not benefit from noncrop vegetation, farms will need to be carefully comanaged for competing conservation and production objectives.

Seed dispersal, interacting with environmental disturbance and management across heterogeneous landscapes, results in irregular weed spatial distributions. Describing, predicting, and managing weed populations requires an understanding of how weeds are distributed spatially and the consequences of this distribution for population processes. Semivariograms and kriged maps of weed populations in several fields have helped describe spatial structure, but few generalizations can be drawn except that populations are aggregated at one or more scales. Limited information is available on the effect of weed arrangement, pattern, or field location on weed population processes. Because weeds are neither regular nor uniform in distribution, mean density alone is of limited value in estimating yield loss or describing population dynamics over a whole field. Sampling strategies that account for spatial distribution can increase sampling efficiency. Further research should focus on understanding processes that cause changes in spatial distributions over time to help predict rates of invasion and potential extent of colonization.

We show that the stability surface that governs the synchronization of a large class of arrays of identical oscillators can be probed with a simple array of just three identical oscillators. Experimentally this implies that it may be possible to probe the synchronization conditions of many arrays all at the same time. In the process of developing a theory of the three-oscillator probe, we also show that several regimes of asymptotic coupling can be derived for the array classes, including the case of large imaginary coupling, which apparently has not been explored.

Weed seedbanks have been studied intensively at local scales, but to date, there have been no regional-scale studies of weed seedbank persistence. Empirical and modeling studies indicate that reducing weed seedbank persistence can play an important role in integrated weed management. Annual seedbank persistence of 13 summer annual weed species was studied from 2001 through 2003 at eight locations in the north central United States and one location in the northwestern United States. Effects of seed depth placement, tillage, and abiotic environmental factors on seedbank persistence were examined through regression and multivariate ordinations. All species examined showed a negative relationship between hydrothermal time and seedbank persistence. Seedbank persistence was very similar between the two years of the study for common lambsquarters, giant foxtail, and velvetleaf when data were pooled over location, depth, and tillage. Seedbank persistence of common lambsquarters, giant foxtail, and velvetleaf from October 2001 through 2002 and October 2002 through 2003 was, respectively, 52.3% and 60.0%, 21.3% and 21.8%, and 57.5% and 57.2%. These results demonstrate that robust estimates of seedbank persistence are possible when many observations are averaged over numerous locations. Future studies are needed to develop methods of reducing seedbank persistence, especially for weed species with particularly long-lived seeds.