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Self-organization in a system of coupled nonlinear oscillator


G.M. Aldonin, V.V. Cherepanov, O.L. Yarygina

For physical systems of different nature is characterized by non-linear phenomena that generate deterministic chaos as a wild card. On the other hand for them, as open systems, characterized by self-organization. Knowledge of the mechanisms of self-organization will investigate the structural organization of deterministic chaos in the radio, in biological, natural and social phenomenons. Common open system is a hierarchy of periodicities in their evolution as a system of coupled nonlinear oscillators (SCNO), which form the structure, due to which it is possible to present a model Fermi–Pasta–Ulam (FPU), which gives a description of the behavior of SCNO as fractal structures with a scale-invariant self-similarity as an n-dimensional torus. Conditions of formation of structural stability SCNO as n-dimensional torus explains Kolmogorov–Arnold–Moser (KAM theorem) as irrational frequency ratio n-dimensional torus, which generates the Fibonacci series. The Fibonacci sequence is the fundamental law of the scale of self-similarity of structural and sustainable in nature and explains the connection of the spectra of type 1/f (the so called spectrum. Flicker noise) with the harmonic self-organization of natural systems. Versatility flicker noise appears in the electrical, physical, chemical, environmental, social, and biological processes and it is recognized as a fundamental property of natural processes. This approach allows us to go from the currently existing phenomenological description of the spectral characteristics of the form 1/f, typical of many natural phenomena, to physical and mathematical models in the analysis of self-organization processes. For example, it is interesting to establish the structural properties of chaos in the mix signal to noise ratio (s/n) in navigation systems, the nonlinear transformations of the signals there are signs of chaotic behavior, as self-organization s/n in PFI as a system of coupled nonlinear oscillators in the form of a self-similar fractal structure. As solitons and autowave processes basis of biological systems, for which the inherent hierarchy of cyclic interactions. Self-organization can also be explained by the automatism of the pacemaker by auto-wave model. SCNO similar model can be used to describe a wide range of systems, for example, to describe the spectrum of electromagnetic and acoustic waves in the parametric radio systems, catastrophic events in large power systems with power fluctuations of individual consumers in the network, the crisis in the global economic system in volatility of the stock market currencies and securities, etc.

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