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5544241047
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note
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In [36], Mirollo and Strogatz speak of positive feedback but this effect plays no role in the demonstration of their theorem. This is why the case of linear oscillators seemed to be excluded from synchronization by their theorem.
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63
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5544258719
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note
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In [36] Mirollo and Strogatz explicitly state the absorption rule but only for a system with numerous oscillators. Since their proof of synchronization is inductive with the system of two oscillators as anchor it is important to realize that absorption is actually necessary for synchronization also for a pair of oscillators.
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64
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85087580292
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In [55], Christensen concluded also that synchronization requires
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c≥1/N.
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c≥1/N
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65
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note
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By adaptation of the frequencies we mean as in [12] a "learning" mechanism, where the oscillators are allowed to modify their intrinsic frequencies in order to match with an exterior periodic stimulus.
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66
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5544230069
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note
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Synchronization with a general shape E(φ) has been also recently proven by Corral et al. [38] in the case of oscillators with adequate response function to pulses. A response function chosen so that the phase advance caused by a pulse gets larger towards the threshold is equivalent to a convex E(φ).
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