Delayed feedback control of noise-induced patterns in excitable media

We show that characteristic features of noise-induced spatiotemporal patterns in excitable media can be effectively controlled by applying delayed feedback. Actually, by variation of the time delay and of the strength of the feedback one can deliberately change both spatial and temporal coherence, as well as adjust the characteristic time scales.

Figure 1

(Color online) (a),(c) Space-time plots of $u(x,t)$ in logarithmic scale, (b),(d) spatially averaged inhibitor concentration $\overline{u}\left(t\right)$ (shaded), for the Oregonator model Eqs. (1). (a), (b) No delayed feedback. (c), (d) Delayed feedback force $F\left(t\right)$ as in Eq. (7) with $K=0.3$ and $\tau =5.25$ is applied to the whole medium [see white vertical stripes in (c)]. In (d) the control force $F\left(t\right)$ is also plotted (dashed line, red online).

Figure 2

(a) (Color online) Average interspike time $⟨T_i⟩$, found numerically (black circles) and estimated analytically (grey-green online dashed line). (b) Normalized fluctuation $R_T$ of the interspike intervals. (c) Mean duration of spikes $⟨{\Delta }_i⟩$. Feedback strength is fixed at $K=0.2$.

Figure 3

(Color online) Bottom graph: a schematic space-time plot of noise-induced patterns: black areas indicate the excited state, grey (green online) areas the refractory state, and hatched areas indicate where the positive feedback is applied. Top graph: the respective profiles of $v\left(x_0\right)$ and of feedback force $F$.