In the context of this book, adaptation is taken to mean a feature of a system aimed at achieving the best possible performance, when mathematical models of the environment and the system itself are not fully available. This has applications ranging from theories of visual perception and the processing of information, to the more technical problems of friction compensation and adaptive classification of signals in fixed-weight recurrent neural networks. Largely devoted to the problems of adaptive regulation, tracking and identification, this book presents a unifying system-theoretic view on the problem of adaptation in dynamical systems. Special attention is given to systems with nonlinearly parameterized models of uncertainty. Concepts, methods and algorithms given in the text can be successfully employed in wider areas of science and technology. The detailed examples and background information make this book suitable for a wide range of researchers and graduates in cybernetics, mathematical modelling and neuroscience.

The last few years have seen an extraordinary growth in many areas of complex systems. In the field of synergetics and cooperative behaviour in neural systems a new vocabulary emerged to describe discoveries of wide-ranging and fundamental phenomena, like for example artificial life, biocomplexity, cellular automata, chaos, criticality, fractals, learning systems, neural networks, non-linear dynamics, parallel computation, percolation, self-organization.One of the contributing factors to this growth is the extraordinary increase in computing power. Previously intractable non-linear systems are now amenable to analysis and simulation and parallel computers are ever more important in these areas.The book contains papers exploring many aspects of complex systems, covering theory and applications and deal with material drawn from many different disciplines and specialities.

In this work, I consider the possibility of using typicality-type arguments for understanding intractably complex damped-driven dynamical systems. By approximating such dynamics with appropriately constrained random process, I illustrate quantitative predictive power for some aspects of the motion. In particular, I argue that local dynamical stability, or exit rate, of a state is typically sufficient to predict steady-state probability in such systems -- circumventing the classic no-go theorems via our disorder approximation. I then focus on one consequence of this result: that the most likely long-time configurations should also be the dynamically stable ones. In a strongly-driven system, however, such stability may be hard to achieve, and therefore has interesting implications about the corresponding configurations: they must be well-adapted to the details of the driving forces, their dynamical robustness may be viewed in the context of self-healing, and depending on the drive, they can require substantial collective fine-tuning among the system's degrees of freedom. I confirm the emergence of such adapted states in several example systems, both in simulation and in experiment, and verify a quantitative agreement with the predicted scaling between their steady-state probability and local stability. I then explore several arguments and test-cases suggesting further generality of this framework. While it is not yet clear what the precise limits of applicability are for this approach, our results suggest that the intuition it builds can help with prediction and design in a broad class of complex dynamics.

This solid introduction uses the principles of physics and the tools of mathematics to approach fundamental questions of neuroscience.

"The emphasis on change at many levels of organization is critically important as is the first attempt to integrate sophisticated theory and research in organization psychology (e.g., Gersick, Hackman) with social psychological models of development such as Moreland and Levine." --Reuben M. Baron, Emeritus, University of Connecticut "Arrow, McGrath, and Berdahl′s ′Small Groups as Complex Systems′ will change the way you think about groups, the way you think about research, and even the way you think about science." --Donelson R. Forsyth, Psychology, Virginia Commonwealth U "The book is excellent, one of those very rare works that will have substantial impact on the field. I would use the book without hesitation in any advanced graduate seminar dealing with groups." --Donelson R. Forsyth, Psychology, Virginia Commonwealth U "A conceptually elegant analysis of groups as systems. Although the systems approach has been growing more influential in various fields of social psychology in the last ten years, no one has put forward a definitive analysis that applies with fidelity the general systems approach to group processes. McGrath and his colleagues fill that gap, not by paying lip service to popular scientific concepts such as recursive causality, open systems, attractors, and complexity theory, but by fully integrating these concepts into their no-nonsense analysis of such group level processes as formation, task performance, composition, development, and termination. Empirical work is folded into the theoretical mix along the way, but the focus is unrelentingly conceptual with the result that the authors deliver on their promise of developing a powerful, unified theory of group dynamics." --Donelson R. Forsyth, Psychology, Virginia Commonwealth U "Theirs is an ambitious book. They have profound ramifications for experimental social psychology. It is worth mentioning that AMD (Arrow, McGrarth, and Berdahl) list an ethnographic approach, which often implies the adoption of hermeneutic and semiotic methods (a hallmark of the anti-Enlightenment tradition in psychology), as a possible way forward." --Yoshihisa Kashima, American Journal of Psychology What are groups? How do they behave? Arrow, McGrath, and Berdahl answer these questions by developing a general theory of small groups as complex systems. Basing their theory on concepts distilled from general systems theory, dynamical systems theory, and complexity and chaos theory, they explore groups as adaptive, dynamic systems that are driven by interactions among group members as well as between the group and its embedding contexts. In addition, they consider not only the group′s members and their distribution of attributes, but also the group′s tasks and technology in order to understand how those members, tasks, and tools are intertwined, coordinated, and adjusted. Throughout the book, the authors focus our attention on relationships among people, tools, and tasks that are activated by a combination of individual and collective purposes and goals that change and evolve as the group interacts over time.

Helping us understand our complex world, this book presents key findings in quantitative complex system science. Its approach is modular and phenomenology driven. Examples of phenomena treated in the book include the small world phenomenon in social and scale-free networks; life at the edge of chaos; the concept of living dynamical systems; and emotional diffusive control within cognitive system theory. Each chapter includes exercises to test your grasp of new material. Written at an introductory level, the author provides an accessible entry for graduate students in physics, mathematics, and theoretical computer science.