Phase fronts and synchronization patterns in forced oscillatory systems Academic Article uri icon

abstract

  • This is a review of recent studies of extended oscillatory systems that are subjected to periodic temporal forcing. The periodic forcing breaks the continuous time translation symmetry and leaves a discrete set ofstable uniform phase states. The multiplicity ofphase states allows for front structures that shift the oscillation phase by[n where n 1, 2,..., hereafter [nfronts. The main concern here is with front instabilities and their implications on pattern formation. Most theoretical studies have focused on the 2" 1 resonance where the system oscillates at half the driving frequency. All front solutions in this case are -fronts. At high forcing strengths only stationary fronts exist. Upon decreasing the forcing strength the stationary fronts lose stability to pairs of counter-propagating fronts. The coexistence of counter-propagating fronts allows for traveling domains and spiral waves. In the 4:1 resonance stationary -fronts coexist with /2-fronts. At high forcing strengths the stationary -fronts are stable and standing two-phase waves, consisting of successive oscillatory domains whose phases differ by, prevail. Upon decreasing the forcing strength the stationary -fronts lose stability and decompose into pairs ofpropagating ]2-fronts. The instability designates a transition from standing two-phase waves to traveling four-phase waves. Analogous decomposition instabilities have been found numerically in higher 2n" 1 resonances. The available theory is used to account for a few experimental observations made on the photosensitive Belousov-Zhabotinsky reaction subjected to periodic illumination. Observations not accounted for by the theory are pointed out.

publication date

  • January 1, 2000