Response of the negative feedback oscillator module. The response R∗(solid line) is shown for a (A, B, E and F) gradient signal and a (D) localized signal input. (A,D) The profiles are shown at a snapshot in time. R∗exhibits irregular spatial oscillations when the signal is in the oscillatory regime and the profile is smooth in regions where the signal is outside of this critical range. (B) This plot illustrates the variation of concentration of the response with respect to time at two spatial locations: the middle of the domain (dashed line) and at the boundary (solid line). The response only exhibits temporal oscillations in the regions where the signal is in the critical oscillatory range. (C) The phase plot is shown for X∗at two adjacent points in the domain. It depicts a densely filled region highlighting the quasi-periodic nature of oscillations. (E) When Y is weakly diffusible, the spatial profile of the response becomes smooth and (F) periodic oscillations in time are observed in the middle of the domain (solid line) whereas in the non-diffusible case they are absent in that region (as seen in (B)).