14 problems

An endotactic reaction network is a reaction network whose embedded reaction graph has the endotacticity property; a $\kappa$-variable mass-action system is one whose reaction rate…

An endotactic mass-action system is a mass-action system whose reaction network is endotactic, and a system is permanent when its trajectories remain uniformly separated from the b…

Let $(\mathcal{X},\mathcal{C},\mathcal{R},\kappa(\tau))$ be a mass-action system with bounded kinetics, governed by … where $0<\varepsilon<1$ and…

A mass-action system $(G,\boldsymbol{\kappa})$ has associated ODEs and is permanent if, on every compatibility class, all solutions eventually enter a compact set that remains attr…

Four-limit-cycle conjecture. There exist parameter values for which the unique positive equilibrium is asymptotically stable and is surrounded by four limit cycles $\Gamma_0$,…

Let a variable-$k$ mass-action system be a mass-action system whose rate coefficients are bounded above and below by positive constants, and let an endotactic mass-action system be…

Fang–Gao's Lyapunov function PDE conjecture. For any MAS that admits a stable positive equilibrium, if the boundary complex set is equipped properly, then the induced Lyapunov func…

Let $n\geq 1$ and consider the multiple futile cycle network with substrates $S_0,\ldots,S_n$ and enzymes $E$ and $F$, in which $E$ facilitates the forward transitions and $F$ the…

A weakly reversible network is a chemical reaction network whose reaction graph has the property that every reaction lies in a strongly connected component. A positive steady state…

Generalized mass action conjecture. Theorem $$ should also hold for generalized mass action systems.

Boundedness conjecture. All trajectories of weakly reversible mass-action systems are bounded.

Persistence conjecture. Any weakly reversible mass-action system is persistent.

Permanence conjecture. Endotactic $\kappa$-variable mass-action systems are permanent for any number of species.

Persistence conjecture. Any weakly reversible mass-action system is persistent.