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Multiplicity of phase states within frequency locked bands in periodically forced oscillatory systems may give rise to front structures separating states with different phases. A new front instability is found within bands where ω f orcing /ωsystem = 2n (n > 1). Stationary fronts shifting the oscillation phase by π lose stability below a critical forcing strength and decompose into n traveling fronts each shifting the phase by π/n. The instability designates a transition from stationary two-phase patterns to traveling n-phase patterns.

This is a study of the nonlinear interactions of solitary waves or impulses in homogeneous, extended media. We obtain the set of ordinary differential equations for the positions of the impulses in the nearest-neighbor approximation. Solutions with constant velocity lead to pattern maps that give the successive spacings of the impulses. From among the infinitely many metastable patterns given by the maps, the system chooses one asymptotically through a hierarchical evolution.PACS numbers: 05.45.+b, 82.40.Fp In this Letter we study spatiotemporal complexity in traveling-wave patterns. We consider extended systems with translational invariance that admit the propagation of solitary waves at constant velocity. Behind our work lie theories of defects in systems with broken, discrete symmetries, 1,2 of wave patterns in excitable media, 3 and of dynamical systems. 4 This work is especially applicable to excitable systems such as the Belousov-Zhabotinskii medium, 5 and cardiac fibers and axons that propagate action potentials. 6 We illustrate the questions of interest with a simple model of an excitable medium 7 " 9 ev t = ~ w + 3v -v 3 + v x w t =v •

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