Spiral instabilities in media supporting complex oscillations under periodic forcing

Abstract

The periodically forced Brusselator model displays temporal mixed-mode and quasiperiodic oscillations, period doubling, and chaos. We explore the behavior of such media as reaction-diffusion systems for investigating spiral instabilities. Besides near-core breakup and far-field breakup resulting from unstable modes in the radial direction or Doppler-induced instability (destabilization of the core's location), the observed complex phenomena include backfiring, spiral regeneration, and amplitude modulation from line defects. Amplitude modulation of spirals can evolve to chambered spirals resembling those found in nature, such as pine cones and sunflowers. When the forcing amplitude is increased, the spiral-tip meander evolves from simple rotation to complex petals, corresponding to transformation of the local dynamics from simple oscillations to mixed-mode, period-2, and quasiperiodic oscillations. The number of petals is related to the complexity of the mixed-mode oscillations. Spiral turbulence, standing waves, and homogeneous synchronization permeate the entire system when the forcing amplitude is further increased.