### Synergetics

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The passengers hurry to get here or there, and the increase of over-crowding after the arrival of the next train could be seen as an analogy of energy inflow. Be it only a limited number of the same people in the hall having no appointments, they would undertake a random walk around and perhaps even a pleasant talk instead. But if, on the other hand, the inflow of passengers would rise further and the mutual.

And this is not mainly due to their mental abilities. They adapt to each other just like real material particles can do. As a result, a unified stream arises which averages the impulses of the strongest and the weakest members of the crowd to a certain generally acceptable and effective movement. Sometimes a direction and a path of one of the streams may suddenly change.

These are typical fluctuations micro-deviations and bifurcations branching of possible ways to which fluctuations may lead. Yesterday I was pushed by a particular lady, today by another one, but their trajectories remain the same. Our brave path-finder has taken another train long ago, but the stream still follow his steps. People change, the structure is being maintained.

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To be more precise in our case, we have here two confronting dynamic structures originating from two crowds which form a stable pattern of their interaction. Indeed, the streams are not rigid and can fluctuate, but there are paths which they objectively and persistently tend to. They can switch over a certain discrete spectrum of paths attractors. It is determined by a design of the metro station. If its configuration and size differ, the patterns are different too. People flow through a structure, generating and sustaining it, and are subordinated to it at the same time.

This is called the slaving principle in synergetics. You may wish to go your own way through the crowd, but to get quicker and to save your energy, you have to follow the stream. As to human systems, a purposive communication could be introduced. The people may wish not to act as material bodies and manage themselves in a more sophisticated way, which interferes with the original spontaneous self-organization and adds a higher degree of complexity to the system.

Finally, it is synergetics that reveals some essential similarities between animate and inanimate systems. It shows that structures themselves may display features of self-preservation and purposive quasi-conscious activity as separate from those of their elements. It could thus happen that new barriers, installed to do away with the constant turmoil in the station, once in a night disappear in a mysterious way. Synergetics as a field of scientific research has existed for over thirty years already. It is widely used, but still not generally accepted.

Sometimes they are used as identical with the former two, and sometimes only partly overlap with them.

## Synergetics of brain function.

Synergetics can be considered as a modern stage of development within the traditions of cybernetics N. Wiener, W. Ashby and system-structural analysis attempts to elaborate the general theory of systems. However, many elements of the latter have undergone further essential reformation. While cybernetics elaborates algorithms and methods of control of systems, synergetics investigates the processes of self-controlling and self-organization of complex systems in the world.

The focus of synergetic research program is to reveal some general laws of self-organization and evolution which are common to processes of quite different nature: physical, chemical, biological, psychological, social. As such synergetics contains an open trend towards universalization and directly borders on philosophy whose aim is to deal with the ultimate features and laws of reality.

General line of synergetic research consists mostly of two elements: from a concrete, but fundamental model of processes to interdisciplinary generalizations and back to concrete subject with its rectified theoretical understanding. Accordingly, synergetics functions as applied synergetics and synergetics proper. The whole history of development of the theory of self-organization shows that significant theoretical generalizations appeared from rather narrow, but fundamental scientific results. The non-equilibrium thermodynamics and the theory of dissipative structures developed by the Brussels school of the Nobel prize winner I.

Prigogine had its background in investigation of processes in physical chemistry. The development of the theory of cooperative behaviour, made by H. Haken and called by himself synergetics proper, originated from the investigations of the coherent radiation of lasers. Lasers became a paradigmatic example of synergetics.

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## Contact Synergetics

Haken is an editor of a Springer series of books on synergetics already more than 60 volumes presenting a whole spectrum of synergetic developments in the world. Mandelshtam and A. Some astonishing results have been obtained recently by the Moscow synergetic school at the Keldysh Institute of Applied Mathematics Russian Academy of Sciences led by S.

Kurdyumov with whom I have been collaborating for more then 10 years. The basic model is here a certain class of nonlinear equations describing evolutionary processes of burning in very fast, so-called blow-up, regimes in dissipative media. The model implies a profound sense.

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Some general features of the complex systems behaviour are being revealed, namely: mechanisms of localization processes structures formation in open dissipative media, spectra of structure-attractors as the most stable formations which evolutionary processes in such media go to; methods of resonant excitation of structure-attractors; way of a complex whole construction from parts structures developing with different speeds.

Laszlo, President of the International Society for the Systems Sciences and a Member of the Club of Rome, is involved in finding ways of a transdisciplinary unified theory construction. The American scholar B. Mandelbrot elaborates the so-called theory of deterministic chaos, various scenarios of transition to chaos and back. The Chilian biologists H.

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Maturana and F. Varela introduced the notion of autopoiesis which, in their opinion, describes a fundamental ability of living beings to permanently maintain their organization and to develop. Varela is working now in Paris and develops the theory of autopoiesis and its application to the human brain activities. The other scholar working in Paris E.

## Synergetics Corporation

Morin, a founder of Association of Complex Thinking Association de la Pensee Complexe , has undertaken profound analyses of the very language of complexity and chaos. There are many other researchers fruitfully working in the fields. All these trends are coloured in specific tones of the original disciplines, e.

The theory deals with such questions as: 1 how does a complex structure arise, i. Synergetics reveals the creative role of chaos in the process of origin of complex structures and their evolution. Chaos manifests itself as a mechanism underlying an exit to one of evolutionary structure-attractors.

The macro-organization evolves from a disorder, chaos on micro-level. One of the most essential questions is that of the trends of evolution: where do evolutionary processes go to? How does history flow on? The future states of complex systems escape our control and prediction. Synergetics coordinates are a set of triangular coordinates in their plane or their generalization to tetrahedral coordinates in space, or the analogs in higher dimensions. In the plane, coordinates are measured along three axes , , and , with the -axis oriented downward and the and axes oriented at angles to each other as illustrated above left figure.

Interpreting , , and as points on the sides of an equilateral triangle obtained by parallel-displacing from the origin three pairs of lines oriented at angles with respect to one another, the coordinates can be interpreted as specifying a given equilateral triangle right figure. A nice property of these coordinates is that the vertices of the triangle obtained by parallel-displacing by are given by , , and see above figure , so that the sums of the coordinates of the vertices are always zero.

This property also holds when the coordinates are generalized to three and higher dimensions. The synergetics coordinates also have the property that the edge lengths of the equilateral triangle described by is precisely , which again generalizes to higher dimensions. Synergetics coordinate provide a convenient way to construct regular circle and sphere packings.

For example, the ring of circles illustrated above at left can be generated by picking all sets of integer synergetics coordinates that sum to zero and such that the sum of the absolute values of the three coordinates divided by two equals one Nelson.

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Similarly, the second ring of circles can be obtained from all sets of integer coordinates that sum to zero and such that the sum of the absolute values of the three coordinates divided by two equals one. The zeroth, first, and second rings are illustrated above at right. Similar properties hold in three dimensions, where appropriate sets of synergetics coordinates give successive shells in a regular sphere packing Nelson , illustrated above.