Model for line defects in complex-oscillatory spiral waves.

Spiral waves in period-doubled and other complex-oscillatory media possess line defects across which the phase of the oscillation changes by multiples of 2pi. For such systems, the concept of a splay state, introduced for coupled oscillator systems, is generalized to an Archimedean spiral splay field. In this splay field a spiral wave in a two dimensional space is considered to be a special splay state where spatial points having identical phase space orbits take phases determined by the Archimedean spiral on which they lie. Using the Archimedean spiral splay field, an equation that determines the shape of the line defect is derived.