6 problems

In the predator-prey system, let $c_e$ denote the habitat shift speed and let the predators' initial decay condition be as specified in the preceding spreading-speed analysis. Assu…

Let $\{(Z_n,\widetilde{Z}_n)\}_{n\in\mathbb{N}_0}$ be a PP-2SDDBPO, with total population variables $T_n$ and $\widetilde{T}_n$, parameter $\mu$, and positive initial values…

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

Consider the problem of proving the existence of a big stable limit cycle in the predator-prey system, and suppose that an appropriate annular region can be used to study the phase…

Consider a predator-prey system with a unique positive equilibrium. The local-global stability conjecture. Local stability of the positive equilibrium should be equivalent to its g…

Let $X_t=(x_t,y_t)$ be the process defined by the Lotka–Volterra PDMP in the paper, with initial condition $X_0=(x_0,y_0)\in\mathbb{R}_{++}^2$. Here, $\mathbb{R}_{++}^2$ denotes th…