In the past two decades the "new science," known popularly as "chaos," has given us deep insights into previously intractable, inherently nonlinear, natural phenomena. Building on important but isolated historical precedents (such as the work of PoincarÃ©), "chaos" has in some cases caused a fundamental reassessment of the way in which we view the physical world. For instance, certain seemingly simple natural nonlinear processes, for which the laws of motion are known and completely deterministic, can exhibit enormously complex behavior, often appearing as if they were evolving under random forces rather than deterministic laws. One consequence is the remarkable result that these processes, although completely deterministic, are essentially unpredictable for long times. But practitioners of "nonlinear science," as "chaos" has become known among experts, recognize that nonlinear phenomena can also exhibit equally surprising orderliness. For example, certain seemingly complex nonlinear systems, involving many interacting components, can exhibit great regularity in their motion, and "coherent structures" - such as the Red Spot of Jupiter - can emerge from a highly disordered background.
Paradigms of Nonlinear Science Researchers in this new nonlinear science have learned to recognize the seemingly contradictory manifestations of chaos and order as two fundamental features of inherently nonlinear phenomena. Indeed, "deterministic chaos" and "coherent structures" are often referred to as two "paradigms" of nonlinear science, in the sense that they represent archetypical aspects of nonlinear phenomena, independent of the conventional discipline in which they are observed. Two other "paradigms" that have emerged from recent studies of nonlinear phenomena can be termed "pattern formation, competition, and selection" and "adaptation, evolution, and learning." It is perhaps most convincing to clarify the impact of these paradigms by presenting examples of their interdisciplinary relevance. The same type of "deterministic chaos" can be observed, for example, in electrical activity from biological systems, in the transition of a fluid to turbulent motion, and in the motion of the moons of the giant planets. "Coherent structures" arise in the turbulent atmosphere of Jupiter, in giant earth ocean waves ("tsunamis"), in the spatial spread of certain epidemics, and, on a microscopic scale, in the behavior of certain unusual solid state materials. "Pattern formation, competition, and selection" occur in very similar ways in such seemingly disparate phenomena as instabilities in secondary oil recovery techniques and laser-plasma interactions in advanced technologies designed to control fusion energy. Recent attempts to isolate the conceptual, as opposed to the biological, essence of life have identified and clarified the paradigm of "adaptation, evolution, and learning" and have led to extensive studies of mathematical models of "neural networks" and to the creation of the field of "artificial life."
Interdisciplinary Nature and Methodology of Nonlinear Science As these examples suggest, nonlinear science is inherently interdisciplinary, impacting upon traditional subjects ranging through all the physical and biological sciences, mathematics, engineering, and many of the social sciences, notably economics and demographics. Any attempt to circumscribe artificially the scope of nonlinear science inevitably limits the insights it can provide. Significantly, the successful pursuit of nonlinear science requires the blending of three distinct methodological approaches: â¦"experimental mathematics," which involves the use of cleverly conceived computer-based numerical simulations to give qualitative insights into problems that are at present analytically intractable; â¦novel and powerful analytical mathematical methods to treat functional recursion relations, to solve certain nonlinear partial differential equations, or to describe complex geometrical structures arising in chaotic systems; and â¦high precision experimental observations of similar nonlinear phenomena in many different natural and man-made systems arising in a variety of conventional disciplines. An important illustration of both this tripartite approach and the interdisciplinary applicability of the paradigms of nonlinear science is the discovery of the metric universality in unimodular one-dimensional maps. Many physicists considered Feigenbaum's results for the universal dynamics of these maps to be a mere mathematical curiosity of no clear physical significance until Libchaber and others observed exactly the same period doubling dynamics in laboratory experiments on fluids and electric circuits. The ensuing efforts to prove various aspects of the theory rigorously have greatly stimulated large segments of the pure mathematics community. Of course, the interaction can also go in other ways; laboratory observations of new nonlinear phenomena have also stimulated and guided the development of theory and mathematical modeling. This close interaction among experimenters, theorists, and pure mathematicians is rare and refreshing in the recent age of increasingly specialized science.
Chaos: An Interdisciplinary Journal of Nonlinear Science The now celebrated example of period doubling illustrates the crucial importance of transferring the developments in our understanding of nonlinear phenomena, wherever these developments occur, to other disciplines. The excitement and challenge of the journal, Chaos: An Interdisciplinary Journal of Nonlinear Science, lie in its interdisciplinary character and its firm commitment to communicating the most recent developments in nonlinear science to the research community at large. We welcome contributions from physics, mathematics, chemistry, biology, engineering, economics, and social sciences, as well as other disciplines in which inherently nonlinear phenomena are of interest and importance. Further, we always seek a balance among the methods of computation, theory, and experiment, to reflect properly the tripartite methodology which has proved essential to the progress of nonlinear science. Finally, Chaos has grown to be truly international in character, again mirroring the field itself.
Uniqueness of Chaos Chaos is a peer-reviewed research journal but with some unorthodox elements relative to typical journals. Besides front-line research papers, letters, and brief reports, Chaos includes solicited technical reviews and deliberately pedagogical articles of broad appeal. The Editors of Chaos take an active role in developing the content and, together with the AIP, seek to assure its comprehensibility, as well as relevance and quality. Importantly, approximately every other issue of Chaos is a special "Focus" issue. These issues are intended to provide a critical introduction and overview of a particular topic, suitable as an introduction to nonspecialists but also of value to experts in the area. To ensure timely publication of other articles, only about 60% of the articles in a "Focus" issue are devoted to the focal topic, with the remaining articles dealing with other areas of nonlinear science. In addition, each article in Chaos is preceded by a "lead paragraph" targeted at the non-specialist reader. This paragraph provides a sense of the context of the work and conveys the primary results, but in language that is accessible to the journal's broad interdisciplinary audience.