Fig.1 Spiral snapshots and spiral tip tractories (a) rfb1=20; (b) rfb1=40; (c) rfb1=60 (The two pink circles are inner and outer boundaries of the annular measuring region. The black dot describes location of the spiral tip before the feedback is switched on. The black line is the tip trajectory after the feedback is applied.)

Fig.2 (a) Tip trajectories at four rfb1; (b) Attractor radius rtip as a function of inner radius rfb1 of a annular measuring region under the control of the feedback signal

Fig.3 (a) Tip trajectories at five h; (b) Variation of rtip with h under the control of a feedback signal

Fig.4 Spiral tip trajectiories under positive and negative gains (a) rfb1=28; (b) rfb1=30; (c) rfb1=40; (d) rfb1=42 (The black trajectories and point attractors are obtained under kfb=0.02, and the case of kfb=-0.02 is illustrated by red color.)

Fig.5 Effect of positive feedback gain on spiral dynamics

Fig.6 Effect of negative feedback gain on spiral dynamics(h=30 and rfb1=42) (a) kfb=-0.015; (b) kfb=-0.02; (c) kfb=-0.025; (d) kfb=-0.035

Fig.7 Transient drift tractories and modular functions of the complex feedback signal

Fig.8 Trajectories of the spiral tip at different dfb1

Fig.9 Trajectories of the spiral tip at different l (a) 2≤l≤20; (b) 21≤l≤46

Fig.10 Effect of kfb on drift trajectiory in the transient phase

Fig.11 Effect of negative feedback gain on spiral dynamics (dfb1=20, l=5) (a) kfb=-0.015; (b) kfb=-0.02; (c) kfb=-0.0225; (d) kfb=-0.025