Abstract
Resonance propagation of radiation in the ionosphere, solar activity, magnetic dynamos, lightning discharges, fracture processes, plastic deformations, seismicity, turbulence and hydrochemical variability are considered as examples of complex dynamical systems in which similar fluctuation and nonlinear oscillation regimes arise. Collective effects in the systems behavior and chaotic oscillations in individual subsystems, the ratio of random and deterministic, the analysis of variability factors and the change of dynamic regimes, the scaling relation between the elements of the system and the interaction of scales are discussed. It is shown that consolidation and branching in disruptions or thunderstorm activity is the transfer of disturbances to up and down of cascades as in turbulence, and the alpha-omega effects of the magnetic dynamo are the same cascade processes, but in the presence of an external magnetic field or rotation that removes the degeneracy in the system by directions. Particular attention is paid to natural generators and oscillation amplifiers, in which the Lorentz triplet plays the role of a universal model of a nonlinear oscillator.
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