10 problems

Let $A^*$ be the interconnection-strength parameter, let $d$ be the transmission delay, and let the values in Table be the numerically identified critical delays at which purely im…

Bistability conjecture. There exists a choice of parameters such that $u^\star$ is locally asymptotically stable but not globally asymptotically stable. The $\omega$-limit set also…

Two-threshold stability conjecture. When

Let the Brusselator be subjected to a noisy term representing a stochastic variation of its bifurcation parameter. Parametric-noise destruction conjecture. Parametric noise destroy…

Consider the stochastic Brusselator system with noise intensity $\sigma>0$. A random equilibrium is a random state invariant under the cocycle dynamics, namely a measurable point…

Consider a delayed single-population model with nine patches, symmetric connectivity matrix $D=(d_{ij})$, patch parameters $(m_j)$ as specified in the example, and multiple Hopf bi…

Let $p_k$ and $p_{\ell}$ be the kinase and phosphatase processivity levels, respectively, and consider oscillations arising from Hopf bifurcations in the ERK system. Oscillation-da…

Let the reduced ERK network be the processive-limit reduction of the original ERK network, and consider the theorem asserting Hopf bifurcations for all processivity levels sufficie…

Consider the random dynamical system induced by the stochastic differential equation in the paper, and fix $a>0$ and $\beta\in\mathbb{R}$. Let $\lambda_{\rm top}$ denote its top Ly…

Consider the two-dimensional stochastic differential equation exhibiting a Hopf bifurcation, with linear stability of the origin as the deterministic Hopf bifurcation parameter and…