Table 2:

Summary of crossover values ${\xi }_{\mathit{\text{lin}}}$. For $\delta x\ll {\xi }_{\mathit{\text{lin}}}$, linear dynamics dominate. For $\delta x\gg {\xi }_{\mathit{\text{lin}}}$, nonlinear dynamics dominate.

Bifurcation type	$\mathit{f}(\mathit{x},\mathit{\mu })$	Fixed points	${\mathit{\xi }}_{\mathit{\text{lin}}}$
linear	$\mu x$	$x^{*}=0$	$\infty$
transcritical	$\mu x-x^2$	$x^{*}=\{0,\mu \}$	$\mu$
saddle node	$\mu -x^2$	$x^{*}=\pm \sqrt{\mu }$	$\pm 2\sqrt{\mu }$
supercritical pitchfork, Hopf	$\mu x-x^3$	$x^{*}=\{0,\pm \sqrt{\mu }\}$	$\{\sqrt{\mu },\pm 2\sqrt{\mu }/3\}$