It is instructive to consider a hydrodynamic stability case where it is found that, according to the linear stability analysis, the flow is stable when R e ≤ ≤ R e c r and unstable otherwise, where R e is the Reynolds number and the R e c r is the critical Reynolds number; a familiar example that is applicable here is the critical Reynolds number, R e c r ≈ ≈ 50 , corresponding to the transition to Kármán vortex street in the problem of flow past a cylinder. The growth rate σ σ r is negative when R e < R e c r and is positive when R e > R e c r and therefore in the neighbourhood R e → → R e c r , it may written as σ σ r = const . × × ( R e − − R e c r ) wherein the constant is positive. Thus, the limiting amplitude is given by