| Abstract: |
| In my talk, I present the dynamics of a laissez-faire predator-prey model with both a specialist and a generalist predator. I analyze the stability of an equilibrium by performing linearized stability analyses. I then reexamine the stability of the equilibrium where the prey and predator coexist by constructing a Lyapunov function. If I hold the generalist predator population constant, treating it as a bifurcation parameter, I show that my model can possess multiple (up to three) limit cycles that surround an equilibrium in the interior of the first quadrant. My model shows rich dynamics including fold, transcritical, pitchfork, Hopf, cyclic-fold, and Bautin bifurcations as well as heteroclinic connections. If I instead vary the generalist predator population slowly across bifurcations, the model exhibits bursting behavior as it alternates between a repetitive spiking phase and a quiescent phase. |
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