Strong structured connectivity with row balance generates high coherence even as chaos persists.

(A) Sample activity of 10 randomly chosen neurons, ϕj, and coherent mode activity, , in black. Strong structured connectivity with row balance subtraction to the random component of connectivity yields chaotic activity that is highly coherent with switching-like behavior. (B) Normalized autocorrelation of coherent mode, , in red. Average normalized autocorrelation of the residuals, qδ (τ), in blue. Shaded regions show standard deviation over 25 initial conditions of the same connectivity. Strong structured connectivity yields coherent mode dynamics that are qualitatively different from those of the residuals. J1 = 15.8 for both (A) and (B), compare to Fig 1C and 1E, respectively. (C) Coherence, χ, as a function of J1 is independent of network size. Coherence appears to approach 1 as J1 is increased demonstrating that chaos persists even as fluctuations in the residuals shrink (See also S4 Fig). Coherence is averaged over 30 realizations of the connectivity for each N, excluding the few fixed points and limit cycles that occur for larger J1 (2 out of 30 or less for the largest values of N). (D) Largest Lyapunov exponent as a function of J1. Thick line shows average over 10 realizations, small dots show values for individual realizations, and shaded region is standard deviation. All but a small fraction of realizations are chaotic, even in the region where χ > 0.9. N = 4000 and g = 2 in all panels unless noted otherwise.