V. Castellanos

collaborators

2 papers

math.DS2026

An intrinsic characterization of the Bogdanov-Takens normal-form coefficients and a mixed-volume obstruction to non-isolated degeneracies

Víctor Castellanos, Ramón Eduardo Chan-López

Let $X$ be a planar vector field with an equilibrium $p$ at which the Jacobian $J = D X (p)$ is nilpotent of rank one, and let $q_{0}$ span $ker J$ . We prove that the two coefficients $…

math.DS2026

Nullcline geometry constrains the location of oscillatory instabilities in planar predator--prey systems

E. Chan-LÃ³pez, E. Chan-López, A. MartÃn-Ruiz +3

We prove that the critical structure of the prey nullcline governs where oscillatory instabilities can emerge in planar predator--prey systems. For a broad class of Gause--type mod…