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math.DS2026
The trace field on the prey nullcline: criticality of planar Hopf bifurcations on the admissible branch
E. Chan-López
Along the prey nullcline of a planar system, the Jacobian entry satisfies , where . Under and predator self-damping, the Hopf trace condi…
math.DS2026
Nullcline geometry constrains the location of oscillatory instabilities in planar predator--prey systems
E. Chan-López, A. Martín-Ruiz, Víctor Castellanos
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…