Crossing-cycle persistence conjecture for tropical polynomial systems

Let a tropical dynamical system have a hyperbolic crossing cycle $\gamma_0$. Crossing-cycle persistence conjecture. For all $0<\epsilon\ll 1$, the associated smooth system has a limit cycle $\gamma_\epsilon$ of the same stability type, with $\gamma_\epsilon\to\gamma_0$ as $\epsilon\to0$. This is a proposed small-$\epsilon$ connection between tropical crossing cycles and limit cycles of the associated smooth system; its validity is left to future work.