16 problems

Let $L$ be a constant migration matrix that is nonsymmetric, and let $\Lambda(m,T)$ denote the growth rate of the corresponding time-periodic system, where $m$ is the migration rat…

Consider the closed-loop system … Let $x_2$ converge to a constant and let $\omega(t,x_2)$ denote the periodic steady-state value approached by $u(t,x)$. Assume that…

Consider periodic systems whose components have different dimensions, in particular spheres joined by linear segments, and let the gap-to-band width ratio refer to the ratio of the…

Characteristic-operator compact-resolvent conjecture. This spectral structure does not always hold: $cDelta(z)$ does not necessarily admit a compact resolvent for every…

Spectral-extension conjecture. The authors conjecture that their results can also yield spectral information for various other classes of periodic linear differential equations, in…

Let $X(-\infty,0)$ and $X(-\infty,T)$ denote the trajectory-history spaces at times $0$ and $T$, respectively, for a linear time-periodic fractional-order differential equation, an…

Assume $a>0>b$ and $a+2b<0$. For the seasonal system denoted by (47ab1), let $\Lambda(m,T)$ be its growth rate, with migration rate $m$ and period $T$. Asymptotic growth conjecture…

Assume $a>0>b$ and $a+2b<0$. For the seasonal system denoted by (47ab), let $\Lambda(m,T)$ be its growth rate, with migration rate $m$ and period $T$. Asymptotic growth conjecture.…

Assume $a>0>b$ and $a+2b<0$, and let $\Lambda(m,T)$ be the growth rate of the three-patch seasonal system under consideration, with migration rate $m$ and period $T$. Upper-bound c…

Assume $a>0>b$ and $a+2b<0$, and consider the three-patch seasonal system described in the source. Let DIG denote dispersal-induced growth. DIG threshold conjecture. DIG does not o…

Let $\mathcal{M}\subset\operatorname{SL}_2(\mathbb{R})$ be the set of real unimodular two-by-two matrices with trace greater than two. Consider discrete systems with modulated coup…

Short-period monotonicity conjecture. There exists $\bar{\omega}>0$ such that, for all $\omega<\bar{\omega}$, the asymptotic outbreak size $1-s^{(\infty)}(\infty)$ is decreasing in…

Katriel's conjecture. When $\nu$ is infinitely small, the inflation threshold satisfies

Let $s(d_I L-V+F)$ denote the principal eigenvalue and let $\mathcal{R}_0(d_I)$ denote the basic reproduction ratio in a time-periodic patch population model, where $d_I$ is the in…

Predator-extinction conjecture. The only feature of the dynamics is predator extinction. Numerical simulations suggest this behavior, but its validity remains an open problem.

Typical trapping conjecture. The trapping property is measurably typical along many curves transversal to the ergodic curves described in the paper.