Fig 1.
(Color online) (a) The tip filament of a scroll wave at the moment t = 200; (b) The circular trajectory of the spiral tip in each layer.
Excitability parameter is ε = 0.04.
Fig 2.
(Color online) The time evolution of the period of spiral waves are plotted from the 1th, 16th, and 32th layer.
Three excitability gradient are illustrated in (a) ε32 = 0.045, (b) ε32 = 0.052, and (c) ε32 = 0.068.
Fig 3.
(Color online) (a) Filament of tips in three dimensional space for the moment t = 200 at ε32 = 0.045. The two lines show the same filament from two different viewpoints. The open circle is the one that projection into the (x, y− plane). (b) The tip trajectory of every layer. (c) The phase filament twist angle of each layer correspond to the top one.
Fig 4.
(Color online) (a) Filament of tips in three dimensional space for the moment t = 500 at ε32 = 0.052; (b) The outward meandering tip trajectories of every layer; (c) The trajectories of the top and bottom layer from the outside to the inside.
Fig 5.
(Color online)(a) Filament of tips in three dimensional space for the moment t = 500 at ε32 = 0.068; (b) The outward meandering tip trajectories of every layer; (c) The trajectories of the first, 16th and the 32th layer along the outward direction respectively.
Fig 6.
The snapshot of the 32th layer at t = 500 with the excitability parameter ε32 = 0.079.
Fig 7.
(Color online)(a) The time evolution of the period of three different layers at ε32 = 0.08; (b) Snapshots of the tip filament illustrating the transition from a stable scroll wave to the onset of its collapse and to turbulent state.
(i)t = 100, (ii)t = 140, (iii)t = 160, (iv)t = 250.
Fig 8.
The chaotic motion in four different layers at t = 250.
(a) the snapshot of the first layer (b) the 10th layer, (c) the 20th layer, (d) the 32th layer. Excitability parameter is ε = 0.08.