Fig. 5. Viability kernels of an hysteretic lake (b = 0.8) for different values of (L_min, P_max). The set of constraints K = [L_min; L_max] × [0; P_max] is bordered by a black rectangle and Viab(K) is colored light gray. (VL_max = 0.1). Varying the pair (L_min, P_max) alters the shape of the viability kernel: if P_max is strictly smaller than the P-values of the equilibria associated with L_min, then the kernel is empty, otherwise, the shape of the kernel depends on the comparison between P_max and the P-values of the equilibria associated with L_min. The curve g defines the right boundary of the viability kernel, and corresponds to a trajectory satisfying u = -VL_max.