Figure 2.

A state portrait of the eco-evolutionary model (3.4) and (3.5). There are three equilibria (a stable node (filled dot) and an unstable focus (empty dot) in region $\mathcal{S}$ and a saddle in region $\mathcal{C}$) and one limit cycle (partly in region $\mathcal{S}$ and partly in region $\mathcal{C}$). There are two attractors, the node and the cycle, and their basins of attraction are separated by the stable manifold of the saddle. There are three sliding segments, one stable (T₁T₂, stretched and magnified in the lower right panel) and two unstable (T₃T₄ and T₅T₆). Predator evolutionary extinction occurs in the dark region. Parameter values: k^u=0.1, k^v=1, r=1, K₀=1, h₀=0.02, h₁=0.02, d₀=0.01, b=0.001, e=0.1, a=5, u₀=1, v₀=3.