“Time-Periodic Forcing of Spatially Localized Structures”
Punit Gandhi is a Postdoctoral Fellow at The Ohio State University, in the Mathematical Biosciences Institute.
Spatially localized structures arise in a number of systems of interest in physics, chemistry and biology. Such states often consist of a steady spatial pattern embedded in a homogeneous background. A localized state that was stable with constant forcing may begin to breathe under time-periodic forcing, i.e., grow for part of the forcing cycle via nucleation of new wavelengths of the pattern followed by wavelength annihilation during another part of the cycle. The parameters of the forcing determine if there will be net growth, a balance, or net decay on average. These distinct dynamics are organized in the parameter space around a series resonances between the nucleation/annihilation time and the forcing period. One motivation for this work comes from considering vegetation patterns in semi-arid environments subject to periodic variation in growth conditions.