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Accumulation boundaries: Codimension-two accumulation of accumulations in phase diagrams of semiconductor lasers, electric circuits, atmospheric and chemical oscillators. (English) Zbl 1153.78324

Summary: We report high-resolution phase diagrams for several familiar dynamical systems described by sets of ordinary differential equations: semiconductor lasers; electric circuits; Lorenz-84 low-order atmospheric circulation model; and Rössler and chemical oscillators. All these systems contain chaotic phases with highly complicated and interesting accumulation boundaries, curves where networks of stable islands of regular oscillations with ever-increasing periodicities accumulate systematically. The experimental exploration of such codimension-two boundaries characterized by the presence of infinite accumulation of accumulations is feasible with existing technology for some of these systems.

MSC:

78A60 Lasers, masers, optical bistability, nonlinear optics
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)
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