Minimal order for explosivity among endotactic stochastic mass‑action systems

Determine the minimal reaction order k for which there exists an endotactic stochastic mass‑action system of order k whose associated continuous‑time Markov chain is explosive.

Background

The paper proves non-explosivity for all second‑order endotactic stochastic mass-action systems, including bimolecular weakly reversible systems. Nonetheless, higher-order examples can be explosive.

A known example shows explosivity at order 10 for a strongly endotactic network, but the smallest order at which explosivity can occur within the endotactic class is not determined.

References

In Example~3.2, an explosive strongly endotactic reaction network of order 10 is constructed. It remains open what is the minimal order for an endotactic stochastic mass-action system to be explosive.

— Non-explosivity of endotactic stochastic reaction systems (2409.05340 - Xu, 9 Sep 2024) in Remark following Corollary 3.2 (Section 3, Non-explosivity)