14 problems

A complex balanced mass-action dynamical system evolves on a positive stoichiometric compatibility class, meaning the set of positive states compatible with the system's conservati…

Global stability conjecture. The equilibria of $\WR0$ systems are globally stable with respect to their compatibility classes.

Consider a mass-action reaction network with stoichiometric compatibility classes determined by its reaction vectors. A system is complex balanced if there is a nonnegative state a…

Global attractor conjecture. Any complex-balanced equilibrium is a globally attracting point within its linear invariant subspace.

A complex-balanced system is a mass-action dynamical system admitting a positive steady state at which the total reaction flow into each complex equals the total reaction flow out.…

Weakly reversible positive recurrence conjecture. All weakly reversible mass-action SRNs are positive recurrent.

Non-product-form conjecture. Then $\mathcal{G}$ has a non-product-form stationary distribution independently of the reaction rate; equivalently, it belongs to class N.

A reaction network $\mathcal{G}$ has complexes in $\mathbb{R}^d$ and stoichiometric subspace $S$; it is strongly endotactic if, for every vector $w\in\mathbb{R}^d$ not orthogonal t…

A weakly reversible mass-action kinetics ODE system is a system whose reaction network is weakly reversible and whose dynamics follow mass-action kinetics. Boundedness conjecture.…

Let $N$ be a confined, weakly reversible reaction system, and let $\mathfrak M(N)$ denote its associated mass-action differential inclusion. Say that $\mathfrak M(N)$ is repelled b…

Let $N$ be a confined endotactic reaction system, and let $\mathfrak M^\ell(N)$ denote its associated differential inclusion. A differential inclusion is permanent when its traject…

Persistence conjecture, bounded-trajectory version. Any weakly reversible reaction network with mass-action kinetics and bounded trajectories is persistent.

Boundedness conjecture. Any weakly reversible reaction network with mass-action kinetics has bounded trajectories.

Let a chemical reaction network be weakly reversible if every reaction belongs to a directed cycle in its reaction graph, and consider its mass-action dynamics on the nonnegative o…