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We study by duality methods the extinction and explosion times ofcontinuous-state branching processes with logistic competition (LCSBPs) andidentify the local time at $\infty$ of the process when it is instantaneouslyreflected at $\infty$. The main idea is to introduce a certain "bidual" process$V$ of the LCSBP $Z$. The latter is the Siegmund dual process of the process$U$, that was introduced in Foucart (2019), as the Laplace dual of $Z$. Byusing both dualities, we shall relate local explosions and the extinction of$Z$ to local extinctions and the explosion of the process $V$. The process $V$being a one-dimensional diffusion on $[0,\infty]$, many results on diffusionscan be used and transfered to $Z$. A concise study of Siegmund duality forregular one-dimensional diffusions is also provided.

Local explosions and extinction in continuous-state branching processes with logistic competition