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Zhalnin A. J. Statistical properties of the intermittent transition to chaos in the quasi-periodically forced system. Izvestiya VUZ. Applied Nonlinear Dynamics, 2006, vol. 14, iss. 5, pp. 30-43. DOI:


Statistical properties of the intermittent transition to chaos in the quasi-periodically forced system

Zhalnin Aleksej Jurevich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences

By the example of the quasi-periodically forced logistic map we investigate statistical properties of the transition from strange nonchaotic attractor to chaos in the system with intermittent dynamics. The probability characteristics of laminar and chaotic phase distributions, as well as scaling laws for distributions of local Lyapunov exponents are studied at parameter values near the transition point. The transition is shown to possess a statistical character and to be associated with the decrease of the average length of laminar phases at nearly constant value of the average length of chaotic bursts. The probability of chaotic phase demonstrate approximately linear increase under variation of the parameter of transition. The distributions of local Lyapunov exponents satisfy common scaling laws for strange nonchaotic and chaotic attractors of intermittent type before and after transition, respectively.

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