Patterns precede processes. They can be interpreted as a memory of the future, a 'remembrance of future activities'. All the attempts that go beyond one of the basins of attraction the 'cones' of attractors are the 'infernal attempts'.
Everything which is not in accordance with the structure-attractors will be wiped out, annihilated. For example, a human can fight unconsciously against those forces some of his attitudes and plans as structure-attractors that 'pull him' from the future, but all these attempts are doomed to failure. However, synergetics shows that the most astonishing events may occur exactly far from equilibrium, i. Localized complex self-organizing struc- tures may appear in such states.
The processes of rapid development were sometimes under investigation in classical science. For example, T. Malthus pro- ceeded in his theory from the supposition that the population on the earth grows in geometrical progression, whereas the resources grow only in arithmetical progression.
It was usually considered and is still sometimes considered that such processes of explosive devel- opment obey the exponential law. The notion is actually one of the misconceptions of classical science. Synergetics investigates conditions for self-organization far from equilibrium and reveals laws of very fast, avalanche-like growth when meta-stable localized complicated structures may emerge.
Such a processes of nonlinear, self-stimulating growth takes place all over the space of a complex system medium , i. As it was already mentioned above, most of the processes, for instance growth of scientific information or sharp upswing of indus- try, occur in blow-up regimes. The processes obey the hyperbolic rather than the exponential law of development.
It is important to understand here how we can initiate such very fast processes in open nonlinear systems and what are requirements for avoiding the probabilistic decay of the complex structures near the moments of their maximal development. The evolution of structures undergoes the periodic change of state from one regime of development to another. There cannot be sharp growth of structure without a threat of fall and destruction. There are some universal laws which govern these rhythms.
They are peculiar to living being as well as to inanimate nature. Only obeying these 'life rhythms', or oscilla- tory modes, can complex systems maintain their integrity and develop dynamically.
The mechanism of the 'self-movement', auto- oscillation, reminds one of the oriental images—the image of Yin- Yang. Yin is complete potentiality and aspiration: the subconscious, the non-verbalized and the hidden. Yang is the realized: the verbal- ized, the revealed. According to the synergetic models used here, changing of the two different, complementary regimes, HS- and LS-modes with peaking, takes place in open media systems with strong nonlinear- ity.
This" could be considered as a mathematical analogy of Yin-Yang alternation, i. HS-mode is a mode of "infinitely running out wave" when there is no localization, all structures, heterogeneities are being washed away.
LS-mode with peaking is a mode of "converging wave of burning", a mode of localization and intensive growth of processes in a more and more narrow area near the maximum. One of the earliest formulations of it may be found in Taoism, in philosophy of Lao Tsu. However, a complete and profound sense of the principle has been revealed only by such theories, as gestalt- psychology, systems theory, and synergetics.
The principle of consideration from the whole to the parts is quite unusual and non-traditional for classical science. The latter moves in the course of analysis mostly from separate parts to a whole. From the synergetic point of view, it is order parameters that determine the behavior of parts subsystems of complex systems.
They allow to reduce enormously the complexity of description of a system under consideration. The classical principle of superposition is not valid in the non- linear world: the sum of partial solutions is not here a solution of equation. The whole is not equal to the sum of its parts. It is qual- itatively different in comparison to parts which are integrated in it.
Besides, an emerging whole alters parts. The coevolution of differ- ent systems means a transformation of all subsystems by mechanisms of system coordination-ordination and correlation between them. Thus, new principles of organization of an evolutionary whole from parts, or the formation of complex structures from simple ones, are discovered by synergetics.
Holism has an evolutionary character in synergetics. A complex structure is an integration of structures of'different ages', that is: structures at the different stages of evolutionary development. The principles which govern the inte- gration of such structures of 'different ages' are gradually being revealed. The integration of simple structures into a complex one occurs by the establishment of a common tempo of development in all unified parts fragments, simple structures.
Structures of "different ages" start to co-exist m one and the same tempo-world. According to this notion, the result of the governing influence is an unequivocal and linear one.
It is directly proportional to the applied energies. It seems that the more energy you put in, the more recoil you get. From synergetics we learn how it is possible to multiply reduce time and efforts needed to generate, by a resonant influence, desired and, what is no less important, feasible complex structures.
Synergetics gives proof of the following thesis: in order to control efficiently complicated systems media , a right topological configu- ration, an 'architecture' of driving mechanism is important, not the intensity of an influence. Weak, but organized in a right topological way—so called resonant,—influences upon complex systems are extremely effective.
The art of soft management consists in the ways of self- management and of self-control of complex systems. How can we push a system in a favorable evolutionary path with a small, resonant influence? How can we provide a system with a self- maintaining and sustainable development? As a matter of fact, the synergetic notions are in accordance with the behavioral rules of Eastern people, first of all, with the principle of non-violence.
Inasmuch as the appearance of nonclassical science was con- nected, first of all, with the birth of the quantum mechanics and the theory of relativity in the first third of our century, the rapid devel- opment of synergetics may be said to represent the next scientific revolution, i. The new paradigm includes a total combination of patterns of non- linear evolutionary thinking as well as certain research approaches.
One may find many non-traditional and highly astonishing notions and ideas in synergetics. Turning the magic crystal of knowledge, the theory teaches us to view the world differently. To sum up, one can express the quintessence of synergetics as a new scientific paradigm by the following theses: 1. Synergetics investigates evolutionary mechanisms and laws of self-organization and coevolution of complex systems of any kind.
Synergetics is interdisciplinary by its character. The synergetic models are heuristic in many disciplinary fields, because they are based on understanding inner mechanisms of behavior of complex systems in general. Synergetics serves as a bridge between the natural sciences and the humanities. The fact has been investigated by the Russian scholar S. Kapitza a as well as by the research team of S.
Kurdyumov Belavin et al. It was shown that the growth of population on the Earth obeys not exponential law, but hyper- bolic law, i. According to the models, we are living already in the period of peaking: the blow-up point is approximately in the year The size of population on the Earth will not certainly reach infinity that year.
It will pass a pronounced maximum and stabilize at its highest point S. I have used this opportunity to add three new chapters on recent developments.
One of the most fascinating fields of modern science is cognitive science which has become a meet ing place of many disciplines ranging from mathematics over physics and computer science to psychology. Here, one of the important links between these fields is the concept of information which, however, appears in various disguises, be it as Shan non information or as semantic information or as something still different. So far, meaning seemed to be exorcised from Shannon information, whereas meaning plays a central role in semantic or as it is sometimes called "pragmatic" information.
In the new chapter 13 it will be shown, however, that there is an important interplay between Shannon and semantic information and that, in particular, the latter plays a decisive role in the fixation of Shannon information and, in cognitive processes, al lows a drastic reduction of that information. A second, equally fascinating and rapidly developing field for mathematicians, computer scientists and physicists is quantum information and quantum computa tion.
The inclusion of these topics is a must for any modern treatise dealing with in formation. It becomes more and more evident that the abstract concept of informa tion is inseparably tied up with its realizations in the physical world. Centered around the natural phenomena of relaxations and fluctuations, this monograph provides readers with a solid foundation in the linear and nonlinear Fokker-Planck equations that describe the evolution of distribution functions.
It emphasizes principles and notions of the theory e. The focus is on relaxation processes in homogeneous many-body systems describable by nonlinear Fokker-Planck equations. Also treated are Langevin equations and correlation functions. Since these phenomena are exhibited by a diverse spectrum of systems, examples and applications span the fields of physics, biology and neurophysics, mathematics, psychology, and biomechanics.
This book, based on a selection of invited presentations from a topical workshop, focusses on time-variable oscillations and their interactions. The problem is challenging, because the origin of the time variability is usually unknown. In mathematical terms, the oscillations are non-autonomous, reflecting the physics of open systems where the function of each oscillator is affected by its environment. Time-frequency analysis being essential, recent advances in this area, including wavelet phase coherence analysis and nonlinear mode decomposition, are discussed.
Some applications to biology and physiology are described. Although the most important manifestation of time-variable oscillations is arguably in biology, they also crop up in, e. The book brings together the research of the best international experts in seemingly very different disciplinary areas. This book, first published in , explores the exciting field of complexity.
For the last several years, the study of interfacial instability and pattern formation phenomena has preoccupied many researchers in the broad area of nonlinear science.
These phenomena occur in a variety of dynamical sys tems far from equilibrium. In many practically very important physical sys tems some fascinating patterns are always displayed at the interface between solid and liquid or between two liquids.
Two prototypes of these phenomena are dendrite growth in solidification and viscous fingering in a Hele-Shaw cell. These two phenomena occur in completely different scientific fields, but both are described by similar nonlinear free boundary problems of partial differential-equation systems; the boundary conditions on the interface for both cases contain a curvature operator involving the surface tension, which is nonlinear.
Moreover, both cases raise the same challenging theoretical is sues, interfacial instability mechanisms and pattern selection, and it is now found that these issues can be solved by the same analytical approach. Thus, these two phenomena are regarded as special examples of a class of nonlinear pattern formation phenomena in nature, and they are the prominent topics of the new interdisciplinary field of nonlinear science.
The transitions from chaos to order, the nature of self-organization, the various approaches to it and certain philosophical inferences are outlined. Synergetics thus represents a remarkable confluence of many strands of thought, and has become a paradigm in modern culture.
This book exposes the reader to striking new vistas in physics and mathematics, chemistry and biology, social sciences and philosophy? Get BOOK. Synergetics Book Description:. They comprise a single work with the sequence of paragraphs numbered to dovetail in a single integrated narrative. They should eventually be published as a single work eliminating the artificial division into two volumes resulting from the chronology of their composition. Applewhite, courtesy of the Estate of R.
Buckminster Fuller. Get BOOK. Synergetics 2. Author : R.
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