We say that two oscillators are synchronised if they are locked to the same frequency Ω. As such, we say that the system is partially synchronised if n < N oscillators are synchronised to the same frequency and is totally synchronised if all N oscillators are synchronised to the same frequency.
Kuramoto found that there is a critical value Kc for the coupling constant such that when K < Kc it is impossible for the oscillators to become synchronised under any circumstances. However, when K > Kc this incoherent state becomes unstable and the system can attain synchrony [8]. As K increases further past Kc more oscillators become synchronised to the one synchronised cluster until K is high enough for the system to reach total synchrony.
The value of Kc depends upon the distribution of the natural frequencies of the oscillators and it is possible to calculate Kc in many circumstances. For example, with a non-trivial Lorentzian distribution of natural frequencies, in the limit n → ∞, Kc is equal to the width of the Lorentzian curve at 0.5 * ymax [4]. One can calculate Kc for other distributions also.
Kuramoto found that there is a critical value Kc for the coupling constant such that when K < Kc it is impossible for the oscillators to become synchronised under any circumstances. However, when K > Kc this incoherent state becomes unstable and the system can attain synchrony [8]. As K increases further past Kc more oscillators become synchronised to the one synchronised cluster until K is high enough for the system to reach total synchrony. The value of Kc depends upon the distribution of the natural frequencies of the oscillators and it is possible to calculate Kc in many circumstances. For example, with a non-trivial Lorentzian distribution of natural frequencies, in the limit n → ∞, Kc is equal to the width of the Lorentzian curve at 0.5 * ymax [4]. One can calculate Kc for other distributions also.
