The considered model of distributed inhomogeneous auto-oscillation medium is described by the one-dimensional nonlinear partial differential equation \[ a_t = i\omega(x)a + r(1 - | a| ^2)a + ga_{xx}, \] where \(i = (-1)^{1/2}\), \(a(x, t)\) is the complex amplitude of oscillations, which depends upon time \(t\) and \(x\) is the spatial coordinate. The nonlinearity parameter \(r\) and the diffusion coefficient \(g\) are supposed constant. The frequency detuning is assumed linear along the spatial coordinate \[ \omega(x) = x\Delta_{\max}/l, \] where \(l\) is the length of the system. Computer simulation reveals formation of frequency synchronization clusters. Cluster boundaries are studied.