4 problems

Let $\bar{\eta}_1$ and $\bar{\eta}_2$ be cumulative-effort constraints satisfying $0<\bar{\eta}_1<\bar{\eta}_2$, and let $\mu_{\alpha_{opt},\bar{\eta}_i}$ be the measures associate…

Assume $\bar{r}_1<0$, $\bar{r}_2<0$, and $\chi>0$, and let $\omega_{crit}(m)$ be the transition frequency for $m\in(0,m^*)$. The curve is understood to extend to the origin with…

Assume $\bar{r}_1<0$, $\bar{r}_2<0$, and $\chi>0$, and let $m^*>0$ be the threshold from the sink-sink result. For $m\in(0,m^*)$, let $\omega_{crit}(m)$ denote the transition frequ…

Let $\Lambda(m,\omega)$ denote the relevant Floquet exponent for dispersal rate $m>0$ and temporal frequency $\omega>0$ in the time-periodic two-patch model, under $\bar{r}_1<0$,…