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arises in analysis of dynamics on an attractor represented by two-dimensional torus and is exploited to study bifurcational mechanisms of break-up of torus with transition to chaos.
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Circle map appears naturally in analysis of periodically kicked non-isochronous self-oscillations in situations when the amplitude perturbation caused by a kick is able to decay completely before appearance of the next kick.
In the parameter plane one can observe a picture of Arnold tongues. Colored domains of periodic regimes (green - period 1, yellow - 2, pink - 3, deep blue - 4, red - 8,…), white - quasiperiodic motion, gray - chaos.
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