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Hyperbolic chaos in a system of resonantly coupled weakly nonlinear oscillators. (English) Zbl 1242.34064
Summary: We show that a hyperbolic chaos can be observed in resonantly coupled oscillators near a Hopf bifurcation, described by normal-form-type equations for complex amplitudes. The simplest example consists of four oscillators, comprising two alternatively activated, due to an external periodic modulation, pairs. In terms of the stroboscopic Poincaré map, the phase differences change according to an expanding Bernoulli map that depends on the coupling type. Several examples of hyperbolic chaos for different types of coupling are illustrated numerically.
34C15Nonlinear oscillations, coupled oscillators (ODE)
34C28Complex behavior, chaotic systems (ODE)
34C23Bifurcation (ODE)
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