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Problem: Consider the autonomous ODE system \begin{align*} \dot{x} &= (1-x) (z-xy)\\ \dot{y} &= \tfrac 1 2 y^2 - (a+xy)(1-y) \\ \dot{z} &= \tfrac 1 2 z^2 - \tfrac 1 2 y^2 + (a+xy)z \end{...

Let $A$ be a real $d\times d$ matrix. The diagonal elements are strictly negative ($a_{ii}<0$) and the off-diagonal elements are non-negative ($a_{ij}\geq 0$ for $i\neq j$). $A$ is strictly column ...

The dynamics $D\ni(r_i,r_{i+1})\mapsto(r_{i+1},r_{i+2})\in D$ on the set $D:=\{(x,y)\in\mathbb{R}^2\colon x>0,y>x^2/2\}$ is given by the recurrence $$r_{i+2}=\frac{r_{i+1}^2}2+\frac1{r_{i+1}^3} ...