7 problems

Fix $k_2>1$. There exist thresholds $k_1^*$ and $k_1^{**}$ with $1<k_1^*<k_1^{**}$ such that the propagation speed $c$ is negative for all $d,r>0$ when $k_1\geq k_1^{**}$, and posi…

Let $k_2>1$ be fixed. Consider the curve in the $(k_1,d)$-plane, for fixed $r$ and $k_2$, on which the propagation speed $c$ is zero. Alzahrani–Davidson–Dodds' monotonicity conject…

Consider the predator–prey system … with parameters near the bifurcation regime $\lambda_1=\lambda_2$, where a cycle exists in one coordinate plane. Suppose the cycle and the assoc…

Consider the predator–prey system … where $s$ is prey biomass, $x_i$ are predator biomasses, and $a_i,m_i,\lambda_i$ are the parameters defined by the nondimensionalisation in the…

Consider the competitive Lotka–Volterra system … … with $a_1<1<a_2$, and let the pulled-regime condition be … where $M=\max\{1,2(1-a_1)\}$. Fix $a_1=\frac12$ and $\sigma=1$. Hosono…

Consider the Lotka–Volterra competition model with parameters $a_1$ and $a_2$, and fix $a_1=0.5$. In the parameter space of this model, the pushed-to-pulled transition curve separa…

Extremal-point conjecture. The set $T$ is a singleton $\{z_0\}$, and the support of the invariant measure that is not supported by one of the two axes is