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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
We work with the trace field restricted to the prey nullcline of a planar predator--prey system and reorganize the first Lyapunov coefficient around this local geometry. For a grap…
math.DS2026
Nullcline geometry constrains the location of oscillatory instabilities in planar predator--prey systems
E. Chan-López, 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…