As t → → ∞ ∞ , the magnitude of the disturbance | A | approaches a constant value that is independent of its initial value, i.e., | A | m a x → → ( 2 σ σ r / l r ) 1 / 2 when t ≫ ≫ 1 / σ σ r . The above solution implies that | A | does not have a real solution if l r < 0 and σ σ r > 0 . The associated solution for the phase function ϕ ϕ ( t ) is given by