Skip to main content
. 2020 Dec 2;30(12):121102. doi: 10.1063/5.0031031

TABLE II.

Categorization of the synchronous states for the case where d0sinα < 0. D0|d0sinα|rj in the last column with rj=rmin for Kmin and rj=rmax for Kmax. Other details are as in Table I. Note the difference in signs of Δ and the boundary values in the additional conditions.

States Oscillators with K from Kmin to Kmax Slope of (Kj,ϕj) Sign(Δ) (R~,D0) Locking range of K Additional condition
S1l0 In-phase synchronous 0 0 R~>D0 [Kmin, Kmax] maxR~,Δ=0
S1l+ Fully locked + R~>D0 [Kmin, Kmax] |Δ|rjR~+D0<Kmin
S1dl+ Drifting–locked + R~>D0 |Δ|rjR~+D0<Kj Kmin|Δ|rjR~+D0
S2l Fully locked + R~D0 [Kmin, Kmax] ΔrjR~+D0<Kmin
S2dl Drifting–locked + R~D0 ΔrjR~+D0<Kj KminΔrjR~+D0
S2d Fully drifting + R~D0 None KmaxΔrjR~+D0
S3l Fully locked + + R~<D0 [Kmin, Kmax] ΔrjR~+D0<Kmin, Kmax<Δrj|R~D0|
S3ld Locked–drifting + + R~<D0 Kj<|Δ|rj|R~D0| ΔrjR~+D0<Kmin, Δrj|R~D0|Kmax
S3dl Drifting–locked + + R~<D0 ΔrjR~+D0<Kj KminΔrjR~+D0, Kmax<Δrj|R~D0|
S3dld Drifting–locked–drifting + + R~<D0 ΔrjR~+D0<Kj<Δrj|R~D0| KminΔrjR~+D0, Δrj|R~D0|Kmax
S3d Fully drifting None + R~<D0 None Δrj|R~D0|Kmin or KmaxΔrjR~+D0
S4d Fully drifting None 0, − R~D0 None ⋅⋅ ⋅