Fig. 2: Overview of the possible transient system dynamics in the presence of a stable equilibrium point.

The transient dynamics of the human consumer-resource system may approach the equilibrium point through damped oscillations (case III; d), or through logistic growth of the human consumer population (case IV; e). At the critical point where the equilibrium becomes stable (a, b), both the baseline and extended model system exhibit sustained oscillations (case III_C; c), just for one unique harvest intensity value (when other parameter are fixed). a State space portrait showing when cases III and IV occur in the baseline model. b State space portrait showing when cases III and IV occur in the extended model. c Temporal dynamics of sustained oscillations. d Temporal dynamics of dampening oscillations. e Temporal dynamics of logistic growth toward the equilibrium. In the dynamics simulations, red lines indicate resource dynamics, whereas population dynamics are shown in green (c), purple (d) and ochre (e), corresponding to the color scheme used in panels a and b. Parameter values (baseline model simulations): Sustained oscillations: c = 0.0088 year⁻¹, h = 0.0044 individual⁻¹ year⁻¹, q = 1.5 individuals #resource units⁻¹; Dampened oscillations: c = 0.0088 year⁻¹, h = 0.0044 individual⁻¹ year⁻¹, q = 1.45 individuals #resource units⁻¹; Logistic growth toward the equilibrium: c = 0.0088 year⁻¹, h =  0.0044 individual⁻¹ year⁻¹, q = 0.13 individuals #resource  units⁻¹; other parameters as in Table 1.