4 problems

Rohr et al.'s conjecture. For mutualistic ecological systems captured by the generalized Lotka–Volterra model, if the interaction matrix $\textbf{A}$ is Lyapunov stable, then…

Let $\Gamma(t)$ be the matrix defined in the paper's Lemma. Asymptotic positive-stability conjecture. There exists $t_1>0$ such that, for every $t>t_1$, the matrix $\Gamma(t)$ is s…

Let $H\foral R^{n\times n}$ be symmetric and entrywise nonnegative, with geometrically simple spectral-radius eigenvalue $\rho(H)$. Let $v,w\in\mathbb R^n$ satisfy $v>0$ and $w>0$.…

Let $A$ be a singular symmetric M-matrix whose eigenvalue $0$ is geometrically simple, and let $v w^T$ be a positive rank-one perturbation. Symmetric singular M-matrix conjecture.…