Segmented Spiral Waves and Anti-phase Synchronization in a Model System with Two Identical Time-Delayed Coupled Layers

In this paper,we consider a model system with two identical time-delayed coupled layers.Synchronization and anti-phase synchronization are exhibited in the reactive system without diffusion term.New segmented spiral waves, which are constituted by many thin trips,are found in each layer of two identical time-delayed coupled layers,and are different from the segmented spiral waves in a water-in-oil aerosol sodium bis(2-ethylhexyl) sulfosuceinate (AOT) micro- emulsion (ME) (BZ-AOT system),which consists of many small segments."Anti-phase spiral wave synchronization" can be realized between the first layer and the second one.For different excitable parameters,we also give the minimum values of the coupling strength to generate segmented spiral waves and the tip orbits of spiral waves in the whole bilayer.