Meron, Ehud Phase fronts and synchronization patterns in forced oscillatory systems. (English) Zbl 0973.35025 Discrete Dyn. Nat. Soc. 4, No. 3, 217-230 (2000). Summary: 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 of stable uniform phase states. The multiplicity of phase states allows for front structures that shift the oscillation phase by \(\pi/n\) where \(n= 1,2,\dots\), hereafter \(\pi/n\)-fronts. 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 \(\pi\)-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 \(\pi\)-fronts coexist with \(\pi/2\)-fronts. At high forcing strengths the stationary \(\pi\)-fronts are stable and standing two-phase waves, consisting of successive oscillatory domains whose phases differ by \(\pi\), prevail. Upon decreasing the forcing strength the stationary \(\pi\)-fronts lose stability and ecompose into pairs of propagating \(\pi/2\)-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 experiment observations made on the photosensitive Belousov-Zhabotinsky reaction subjected to periodic illumination. Observations not accounted for by the theory are pointed out. Cited in 1 Document MSC: 35B10 Periodic solutions to PDEs 35B34 Resonance in context of PDEs 35K57 Reaction-diffusion equations Keywords:periodic temporal forcing; 2:1 resonance; 4:1 resonance; photosensitive Belousov-Zhabotinsky reaction subjected to periodic illumination PDFBibTeX XMLCite \textit{E. Meron}, Discrete Dyn. Nat. Soc. 4, No. 3, 217--230 (2000; Zbl 0973.35025) Full Text: DOI EuDML