Fig. 5.

Renormalized value of the carrying capacity-related parameter b as a function of the coarse-graining scale l. As l increases and coarser levels of description are achieved, an initially negative b can invert its sign for sufficiently small values of the diffusion constant D. This change of sign induces a change in the order of the transition, from discontinuous (at small scales or deterministic level) to continuous (at sufficiently large scales). On the contrary, for large values of the diffusion constant D, b remains always negative, and the transition remains abrupt. Parameter values are $a=1$, $c=0.5$, ${\sigma }^2=1$; initial value of $b=-0.5$; and diffusion constants (from bottom to top) are from $D=2.0$ to $D=0.2$ in equal intervals. A very similar plot can be obtained as a function of ${\sigma }^2$: large noise amplitude values induce a change in the sign of b and, thus, the nature of the phase transition.