Abstract
The characteristic features of transition from regular oscillations to chaotic motion in dynamical systems with finite or infinite dimension of phase space are discussed. It is established that for a specific form of the nonlinearity in these systems, chaotization of motion follows the same autoparametric scenario. The sequence of bifurcation phenomena in this case is the following: state at rest ⇒ limiting cycle ⇒ half-torus ⇒ strange attractor. Based on the results of numerical modeling, we conclude that this scenario is universal. The results of numerical calculations are confirmed by field experiments with radio physical self-oscillating systems.
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Vladimirov, S.N. Autoparametric Scenario of Transition to Chaotic Motion in Dynamical Systems. Russian Physics Journal 47, 547–555 (2004). https://doi.org/10.1023/B:RUPJ.0000046329.92538.f5
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DOI: https://doi.org/10.1023/B:RUPJ.0000046329.92538.f5