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Unfortunately, these perturbations can not be joined continuously to those of the interaction region.
Statistical mechanical implications of these perturbations are described.
Change in the self-system is explained by perturbations in the life of the individual.
Our computations give some evidence that these travelling waves are stable even to large perturbations.
In this case a perfect hexagonal pattern, which is stable under symmetric perturbations, is perturbed asymmetrically.
If, for example, the attractor of the parabolic limit equation is chaotic, then trajectories are sensitive to perturbations.
In experiments and numerical simulations, stable spatially-periodic patterns typically arise through small, localized perturbations of the underlying unstable background state.
Our stability analysis, for perturbations of localized solutions, typically leads to singularly perturbed eigenvalue problems with spatially inhomogeneous coefficients that are difficult to study analytically.
An attractor state is insensitive to (small) perturbations.
The situation in which we apply bump perturbations will often be of the following type.
We are far from understanding how these abnormalities co-operate during tumourigenesis and how such perturbations in cell cycle control could be used clinically.
We now describe the sequence of perturbations that produces the desired metric.
Unlike the smooth expanding maps treated just above, such maps are in general not structurally or measure-theoretically stable with respect to deterministic perturbations.
Moreover, we obtain sharp spectral stability results for deterministic and random perturbations.
In the third flow region, behind the stator there is uniform axial steady flow and zero swirl with downstream-propagating acoustic and vorticity perturbations.
