Fig. 3. Phase diagrams for the ecosystem’s dynamics under open access and profit-maximizing harvesting for low complementarity (σ = 0.95, left diagram) and high complementarity (σ = 0.05, right diagram) between ecosystem services in consumption. Dynamics are characterized by dx/dt > 0 (< 0) below (above) the green line, and dw/dt > 0 (< 0) left (right) of the red line. In the left phase diagram, A is an unstable equilibrium, B and C are locally saddlepoint-stable equilibria, D is the only and (almost) globally stable equilibrium; the corresponding basin of attraction comprises the entire state space with the exception of the axes (x = 0, w ≥ 0) and (x ≥ 0, w = 0). In the right phase diagram, A is an unstable equilibrium, B and C are locally stable equilibria; the corresponding basins of attraction consisting of the areas northeast (B) and southwest (C) of the saddlepath; D is a saddlepoint-stable equilibrium whose basin of attraction is just a one-dimensional line. Parameter values for both diagrams: ρx = ρw = 0.5, κx = κw = 1, γx = γw = 0, νx = νw = 1, α = 0.6, n = 1.


Fig. 3