Fig 1.
Maze solving by P. polycephalum following [4].
Panel (a) shows a schematic of the set-up used by [4], where black color corresponds to inhabitable space for P. polycephalum. Panel (b) shows the abstract graph model of the maze in (a) with nodes in black and edges in blue color. The two food sources N1, N2 are shown in red.
Fig 2.
Schematic of the δD1–δD2 parameter space.
(a) for ϵ < 1/4 and (b) for ϵ > 1/4. Stable equilibria are marked by a red circle, unstable ones by a blue circle; linear stability of the respective equilibria is also indicated by arrows surrounding them. The equilibria are numbered as in Appendix A. Trajectories in the D1–D2 phase-space cannot cross any of the lines drawn; hence the lines divide the phase space into 8 sectors in which trajectories stay for all times. The blue lines are given by D2 = a2,3D1 and divide the basins of attraction of the three (ϵ < 1/4) respectively two (ϵ > 1/4) fix points.
Fig 3.
a) Forcing function Φ(t) for the modified deterministic Tero–Kobayashi model with intermittent lighting and parameters br1 < br2 and β1 < β2. Solid lines show the instantaneous forcing Φ1(t) (red) and Φ2(t) (blue), dashed lines are for the time-averaged forcing as denoted by the angle brackets 〈⋅〉. b) Attractors (markers) and basin of attraction (shaded) for the stable equilibrium with both D1 ≠ 0 and D2 ≠ 0 of the deterministic model. Squares are for the unforced model (dark/dark), circles are for
(light/dark), stars are for
(light/light). Filled symbols denote stable equilibria, hollow symbols stand for unstable equilibria. The shaded region denotes the basin of attraction for the unforced model. The basins of attraction for the forced models are between the corresponding red lines (light/dark) and blue lines (light/light), respectively. The unshaded regions left/right respectively above/below these lines are the basins of attraction for convergence on a single path (D1 = 0 or D2 = 0). We assume here the model is locked forever into the respective forcing regime.
Table 1.
Experimental parameters.
Fig 4.
Comparison of system dynamics.
Evolution of the mean correctness and the variance σ for the full model (black/gray lines; subscript full) and the reduced one-dimensional one (red lines; subscript 1D). Opaque lines show the evolution of cdet, i.e. for the corresponding deterministic system where σ = 0. (a) Poincaré section of the system for ωt = 2πn with
, i.e. at the beginning of each forcing cycle; (b) complete time series for t/(2π) < 5, i.e. the first 50 forcing cycles.
Fig 5.
EFA-estimated drift (a) and noise (b) coefficients of a one-dimensional temporally homogeneous Markov process for each of the three forcing regimes. In (b) the time-weighted average of all three forcing regimes is shown as well.
Fig 6.
Φnorm ≡ (Φ − min[Φ])/(max[Φ] − min[Φ]), and splitting probabilities p±1(c) of the temporally homogeneous process.
Fig 7.
Solutions a1, a2 and a3 for the coefficient a linking D1 and the corresponding three equilibria for ϵ < 1/4. The symbols are equidistantly spaced in the range 0 < ϵ < 1/4 with Δϵ = 0.005. For ϵ ≥ 1/4, only one equilibrium exists which is shown by the dashed black line. Line style indicate the stability of the respective equilibrium where dashed corresponds to unstable and solid corresponds to stable equilibria.