How nature works: the theory of self -organized criticality. 2nd edition. Per tank

Why do you need the theory of complex systems? And how did this author dare to give the book the such loud name: “How does nature work”? The answer is simple and concise - unlike other theories describing certain individual complex systems, self -organized criticality - the first general theory of complex systems based on a solid mathematical foundation. The tank is the discoverer of self -organized criticality - a concept that gains an increasing weight in modern science. It turns out that many, in no way connected, at first glance, with each other, the phenomena - from the formation of the landscape to evolutionary processes, from the activities of the nervous system to economic behavior - have a number of common properties.

Such properties are commonly called emergent. The wave of the “magic wand” of the theory of self -organized criticality illuminated all this diversity and allowed to see the inner unity. What is it manifested in?

Firstly, the property of intermittent equilibrium: long periods of relative rest from time to time are interrupted by disasters ("avalanches") of various scale.

This can be both an avalanche in the literal sense of the word, and a variety of crisis phenomena - mass extinctions of species, collapse and rally of shares, solar flashes or the appearance and disappearance of structures in cellular machines.

Secondly, in the steppe laws: the ratio between the size of the avalanches can be described by a simple exponential formula. No special theories are required for large-scale events-the same forces are responsible for the current decrease in the Dow Jones index by 5 points, and for the Black Monday 1987.

Thirdly, fractal geometry: self-melodies are inherent in the system on any scale. And finally, in the characteristic 1/F-shum, when, with the development of a system in time, the recording of its evolution is also fractal. These features are so similar that, as the author writes, “it makes you think: is it all the manifestations of one principle? Maybe there is a certain analogue of the Newtonian law, its f = that complex behavior? ” The first tank convincingly shows that self -organized criticality is a spontaneous evolution of systems to a critical state - and is the key to understanding this single principle. This popular science book opens up an exciting view of the horizons of tomorrow's science; It is unique in the holistic picture that it creates with the reader gives a guiding thread and a set of basic models that help to understand what is happening and offer tools for describing it, and also helps to rethink the understanding of many events and phenomena of the world. The book is designed for a wide range of readers.