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Cycles of chaotic intervals in a time-delayed Chua’s circuit. (English) Zbl 0890.58052

Summary: We study the bifurcations of attractors of a one-dimensional 2-segment piecewise-linear map. We prove that the parameter regions of existence of stable point cycles \(\gamma\) are separated by regions of existence of stable interval cycles \(\Gamma\) containing chaotic everywhere dense trajectories. Moreover, we show that the period-doubling phenomenon for cycles of chaotic intervals is characterized by two universal constants \(\delta\) and \(\alpha\), whose values are calculated from explicit formulas.

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37B99 Topological dynamics
37E99 Low-dimensional dynamical systems
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