Fig 5. Realization-dependent symmetry breaking in the self-tuned chaotic regime.

(A) Sample traces of coherent mode current, $\overline{h}\left(t\right)$, (top) and histogram of values of $\overline{h}\left(t\right)$ (bottom) from a connectivity realization with real eigenvalue for J₁ = 40,60,80 increasing from left to right. Dynamics exhibit pronounced asymmetry. (B) Absolute value of the time-average coherent mode current, $\mid \langle \overline{h}\rangle \mid$, as a function of J₁. Each colored line represents a single connectivity realization, averaged over 10 initial conditions. For many individual realizations, $\mid \langle \overline{h}\rangle \mid$ is significantly non-zero over a large range of values of J₁, while still not arriving at fixed point value (displayed by dashed line). We display the 37 realizations with real leading eigenvalue out of 100 total realizations from this set of trials. Thick black line shows average over those realizations. Dashed line shows ${\overline{h}}^c={\varphi }^{\prime -1}\left(\frac{1}{g}\right)$. N = 8000 for all panels.