13 problems

Ascending-branch arc localization conjecture. The arc $\mathcal{A}$ is always strictly contained between consecutive critical points of the nullcline.

Geometric localization conjecture. Every coexistence equilibrium at which a Hopf or Bogdanov–Takens bifurcation occurs has prey coordinate in $(x_{\min},x_{\max})$, where…

Spectral-barrier localization conjecture. The localization of such bifurcations holds for general smooth prey nullclines, with critical points acting as spectral barriers that orga…

Conjecture on Type I extinction. The same extinction result should hold for the unbounded Type I functional response as well, although proving it would require different techniques…

Finite-time predator blow-up conjecture. For the delayed system, the predator population explodes to infinity in finite time.

Consider the general predator-pest model … where $x$ is the pest population, $y$ is the predator population, $\xi$ is the quantity of additional food, and $f$ is a pest-dependent f…

Consider the delayed predator-prey system … with $m>0$, delay $\tau\geq 0$, and nonnegative continuous initial data in $C([-\tau,0],\mathbb{R}_+)\times C([-\tau,0],\mathbb{R}_+)$.…

Consider the prey-predator model studied in the paper, with the Bautin bifurcation point $B$ and the associated phase portraits described above. Higher-codimension bifurcation conj…

Consider the predator-prey system of Leslie type with simplified Holling type IV functional response discussed in the paper, and the open problem of proving the existence of a big…

In the stochastic three-species predator-prey model, let $N$ denote the number of small-amplitude oscillations between two spikes, and consider the distribution of $N$ for sample p…

Consider system (2.2) with parameters $r$, $r_0$, $\beta$, and $a$, and let an interior steady state mean a steady state whose components are positive. The interior steady-state co…

Consider the computed population of solutions associated with stable and unstable periodic orbits in the model, and let the moduli space flow constraint and the chosen initial samp…

Let $C_1$ and $C_2$ be the quantities determining the Floquet multiplier $4\lambda4$ of a periodic predator-prey orbit, and suppose external parameters can drive the system, potent…