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Let there be two identical, symmetrically coupled oscillators, denote the phase as If the coupling is pulse coupled with some sort of transfer function The phase dynamics can be described by, Now, in case of phase synchrony, Therefore, is the key function to consider. If this function is 0 at 0, it means there exist a stable synchronizing solution. And 0 at other phase differences implies phase synchrony. Note that this function has the same sign and solution as the odd portion of As says the second derivative of [1] Dong-Uk Hwang, Sang-Gui Lee, Seung K Han, Hyungtae Kook, "Phase-model analysis of coupled neuronal oscillators with multiple connections", Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), Vol. 74, No. 3. (2006) [doi] [2] Hyungtae Kook , Sang-Gui Lee , Dong-Uk Hwang and Seung Kee Han Synchronization of a Neuronal Oscillator Network with multiple connections of time delays Journal of the Korean Physical Society, 2007 50:341-345. [3] Hideyuki Cateau, Katsunori Kitano, Tomoki Fukai, "Interplay between a phase response curve and spike-timing-dependent plasticity leading to wireless clustering", Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), Vol. 77, No. 5. (2008) [doi] |
