Figure 4
From: Period doubling as an indicator for ecosystem sensitivity to climate extremes
Period doubling as an early indicator for ecosystem collapse. Top panel shows the sequence of events and resulting dynamical behaviors along the precipitation axis for different functional groups (obtained from Eq. (2)), beginning with 1:1 (annual) oscillations (green), cascade of period-doubling bifurcations leading to 2n:1 (n = 1, 2, ...) oscillations (light green), chaotic oscillations (yellow), and collapse to bare soil (black solid line). Also shown is the early collapse to bare soil induced by adding a stochastic precipitation component (black dashed line). Panels A–C show power spectra (absolute values of the Fourier transform) for 1:1 periodic oscillations (C), 2:1 periodic oscillations (B) and chaotic oscillations (A). The precipitation rates and functional groups for which these power spectra were calculated are shown by the blue triangles in the top panel. Panels (D–F) show power spectra at increasing distances from collapse to bare soil (see red circles in top panel) for stochastic precipitation. The signatures of period doubling get smaller as the distances increase. Parameters are as in Table 1.
