Near-core spiral instability of spiral waves at . is increased from 0.04 to 0.05 at (a) , (b) , (c) , and (d) . Other parameters: , , . The color bars show the concentration of variable with blue corresponding to low concentration. The system is divided into grid points.
Far-field instability of spiral waves at . is increased from 0.08 to 0.09 at (a) , (b) , (c) , and (d) . [(e)–(g)] Trajectories of the spiral tip when , , and , respectively. All other parameters as in Fig. 1.
Spiral waves demonstrating arm-rupture, homogenous synchronization to reorganization at . is increased from 0.09 to 0.10 at (a) , (b) , (c) , (d) , and (e) . (f) Concentration profile along a cross section of (e) that passes through the spiral tip. (g) Local time series at point h (250, 500) in (c). [(h) and (i)] Phase portraits during two different time periods in (g). [(j) and (k)] Time series corresponding to (h) and (i), respectively. The system is divided into grid points. All other parameters as in Fig. 1.
Pine conelike spirals in the forced system at . increases from 0.08 to 0.09. (a) Trajectory of the spiral tip. (b) Three-dimensional snapshot of spiral at . (c) Two-dimensional rendering of (b). (d) Photograph of a pine cone. All other parameters as in Fig. 1.
Arm splitting and backfiring of spiral waves at . increases from 0.14 to 0.15 at (a) , (b) , (c) , and (d) . All other parameters as in Fig. 1.
Tip meandering and local complex oscillations at . Panels (a1)–(d1) are trajectories of the spiral tip and (a2)–(d2) are the corresponding local time series at point (250, 250). (a1) , (b1) , (c1) , (d1) . All other parameters as in Fig. 1.
Relation between tip movement and local period-2 mixed-mode oscillations. Panels (a) and (b) are two portions of the spiral-tip trajectory in Fig. 6(c1). (c) is the corresponding local mixed-mode oscillations of period 2 at point (250, 250). The arrows in (a) and (b) represent the beginning and ending of the trajectory segments and are located at the same point, where the segments join. All parameters as in Fig. 6.
phase diagram. Frequency-locked (resonant) dynamics appears at line with black dots. Spiral breakup or homogenous synchronization occurs above the line with black triangles. I and II are regions of different tip meandering as shown in the figure. III is region of spiral turbulence or homogenous synchronization. Solid hexagons indicate arm splitting and backfiring spirals. Triangles and squares denote angular amplitude-modulation (pine conelike) spirals and arm-reorganized spirals, respectively.
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