Generality of the dimension-dependent slope trend before the first chaotic peak in fully heterogeneous lattices

Ascertain whether, in fully heterogeneous N-dimensional nearest-neighbor Rulkov neuron lattices, the observed decrease in the slope of the maximal Lyapunov exponent curve approaching the first chaotic peak persists for dimensions greater than four and whether this slope tends to flatten as spatial dimension increases.

Background

For fully heterogeneous lattices with four neurons per dimension, the authors report that the ascent toward the first chaotic peak in the maximal Lyapunov exponent becomes less steep with increasing dimension. This suggests a possible dimension-dependent smoothing of the route into synchronized bursting behavior.

Because the analysis is limited to N ≤ 4 and relies on smoothed data, the authors note uncertainty about whether the trend extends to higher dimensions and whether the slope ultimately flattens, which would have implications for universality and scaling of collective dynamics in high-dimensional discrete-time neuronal systems.