Fig. 5: Independent amplitude coordination in the F-N model.

a The time course of V for the periodic oscillation in the F–N model with NBC. The amplitude is independently increased by varying the coordinator at each time labels t = 200, 400, 600, 800, and 1000. The gaps between each stripes remain invariant. See Supplementary Fig. 12 for the time course of W. b The time course at x* = π/2. c The relation between f₁₁ and f₁₂ of an optimal coordinator for the independent amplitude coordination. The circles (from left to right) represent the policies applied in a as time goes on. When f₁₁ is greater (respectively, less) than zero, the amplitude of the oscillation is increased (respectively, decreased). A critical value exists (approximately r_A = 0.723), below which the oscillation turns out to be unstable. d The average energy consumed by a coordinator to sustain an oscillation at desired amplitude. When suppressing an oscillation (the light gray region), the energy consumption grows rapidly as the amplitude becomes smaller. Contrarily, the energy growth is not significant for magnifying the amplitude (white region). e, f A typical example of amplitude amplification in the F–N model with RBC. e, f show, respectively, the original oscillation and the one with magnified amplitude in (x, V, W, )-space. The dark circles are the projections of parametric orbits (V, W) onto the (V, W)-plane with the greatest amplitude. In each panel, two examples of amplitudes are marked by arrows. The smaller one corresponds to x = 0 while the larger one to the dark circle.