Markedly apart from elementary particle physics, another current has been building up and cont i nuous ly growi ng within contemporary phys i cs for severa 1 decades, and even expanding into many other disciplines, especially chemistry, biology and, quite recently, economics. Several reasons account for this: presumably the most impor- tant one lies in the fact that, whatever the specific problem, model or material concerned, the same basic mathematical features are always involved. In this way, a general phenomenology has emerged which, unlike thermodynamics, is no longer depen- dent upon...

According to its definition, Synergetics is concerned with systems that produce macroscopic spatial, temporal, or functional structures. Autowaves are-a specific, yet very important, case of spatio-temporal structures. The term "autowave" was coined in the Soviet Union in analogy to the term "auto-oscillator." This is - perhaps too literal - translation of the Russian word "avto-ostsillyatory" (= self- oscillator) which in its proper translation means "self-sustained oscillator." These are oscillators, e. g., clocks, whose internal energy dissipation is compensa- ted by a (more or less)...

This volume contains the lectures and contributions presented at the International Symposium on Temporal Order held in Bremen, September 17-22, 1984. Temporal order, such as a more or less regularly repeated temporal sequence of events, can evol ve in open systems far removed from equi 1 i bri um. Progress duri ng the last decade in the analysis and the modelling of this complex phenomenon in both biological and chemical systems gave rise to the idea of a joint conference. The purpose of the symposium was to stimulate future work by enhancing the exchange of experimental and theoretical...

A great deal of the success of science has rested on its specific methods. One of which has been to start with the study of simple phenomena such as that of falling bodies, or to decompose systems into parts with well-defined properties simpler than those of the total system. In our time there is a growing awareness that in many cases of great practical or scientific interest, such as economics or the hu- man brain, we have to deal with truly complex systems which cannot be decomposed into their parts without losing crucial properties of the total system. In addi- tion, complex systems have...

Of the variety of nonlinear dynamical systems that exhibit deterministic chaos optical systems both lasers and passive devices provide nearly ideal systems for quantitative investigation due to their simplicity both in construction and in the mathematics that describes them. In view of their growing technical application the understanding, control and possible exploitation of sources of instability in these systems has considerable practical importance. The aim of this volume is to provide a comprehensive coverage of the current understanding of optical instabilities through a series of...

How well is Nature simulated by the varied asymptotic models that imaginative scientists have invented? B. Birkhoff 52J This book deals with asymptotic methods in nonlinear dynamics. For the first time a detailed and systematic treatment of new asymptotic methods in combination with the Pade approximant method is presented. Most of the basic results included in this manuscript have not been treated but just mentioned in the literature. Providing a state-of-the-art review of asymptotic applications, this book will prove useful as an introduction to the field for novices as well a reference...

Rhythms of the heart and of the nervous and endocrine system, breathing, locomotory movements, sleep, circadian rhythms and tissue cell cycles are major elements of the temporal order of man. The dynamics of these systems are characterized by changes in the properties of an oscillator, transitions from oscillatory states into chaotic or stationary states, and vice versa, coupling or uncoupling between two or more oscillators. Any deviation from the normal range to either more or less ordered states may be defined as temporal disorder. Pathological changes of temporal organization, such as...

Open nonlinear systems are capable of self-organization in space and time. This realization constitutes a major breakthrough of modern science, and is currently at the origin of explosive developments in chemistry, physics and biology. Observations and numerical computations of nonlinear systems surprise us by their inexhaustible and sometimes nonintuitive variety of structures with different shapes and functions. But as well as variety one finds on closer inspection that nonlinear phenomena share universal aspects of pattern formation in time and space. These similarities make it possible to...

Many novel cooperative phenomena found in a variety of systems studied by scientists can be treated using the uniting principles of synergetics. Examples are frustrated and random systems, polymers, spin glasses, neural networks, chemical and biological systems, and fluids. In this book attention is focused on two main problems. First, how local, topological constraints (frustrations) can cause macroscopic cooperative behavior: related ideas initially developed for spin glasses are shown to play key roles also for optimization and the modeling of neural networks. Second, the dynamical...

Synergetic Economics presents a new advance in analytical economics. It deals with problems related to time and change in economic systems, including complex aspects, such as the effects of nonlinearity, instability, bifurcation and chaos in economic evolution. The author argues that economic systems may run through a hierarchy of instabilities in which more and more structural patterns evolve. Such instabilities are caused by changes in the external parameters of the system. They may lead to new spatial-temporal patterns of the system. A number of explicit examples are provided to...