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Abstract
It has been recently shown that the continuous coupling of non-linear oscillators close to an Andronov homoclinic bifurcation generically leads to two types of instabilities: a self-focusing Kuramoto like instability or a finite wavelength period doubling instability. The purpose of this paper is to study simple examples where these instabilities have been observed. It includes the coupling of two pendula, the sine-Gordon chain and the coupling of dissipative non-linear oscillators.
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