Indeterminism in the limit for induced HGRNs

Determine whether, for induced hybrid gene regulatory networks (two discrete levels per gene with celerities determined by a complete weighted directed influence graph), the probability that a randomly initialized trajectory exhibits indeterminism tends to 1 as the number of genes n tends to infinity, analogously to Theorem PC established for general HGRNs.

Background

Theorem PC in the paper establishes that for general HGRNs with at least two discrete levels per gene, when celerities and the starting point are drawn uniformly at random, the probability that a trajectory becomes indeterministic tends to 1 as the dimension grows.

The authors ask whether this asymptotic phenomenon persists under the additional structural constraint of induced HGRNs, where celerities are determined by an influence graph.