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A phase transition induces chaos in a predator-prey ecosystem with a dynamic fitness landscape

Fig 2

The onset of chaos with increasing prey evolutionary rate in a predator-prey system.

(A) As the timescale of the evolutionary dynamics, V, increases relative to the timescales of predator-prey interactions, the system undergoes a Hopf bifurcation from stable limit cycles (upper panel, ) to chaotic cycling (bottom panel, ). (B) The “teacup” strange attractor for the system in its chaotic state (). Projections of the dynamics onto pairs of dynamical variables are shown in the inset. For this figure, a₁ = 2.5, a₂ = 0.05, d₁ = 0.16, d₂ = 0.004, b₁ = 6, , k₁ = 6, k₂ = 9, k₄ = 9, y_a = 8, Simulation time: 4 × 10⁴.

doi: https://doi.org/10.1371/journal.pcbi.1005644.g002