Existence of periodic solutions to a non-autonomous allelopathic phytoplankton model with fear effect

The authors considered a non-autonomous allelopathic phytoplankton competition model that incorporates the influence of fear effects that are often observed in natural biological phenomena. Based on Mawhin's coincidence degree theory, sufficient conditions for the existence of periodic solutions were obtained. The authors validated their findings with an example and simulations showing that the constant coefficient case leads to dynamics that are neither steady state nor $T$-periodic, while the periodic coefficient case generates sustained $T$-periodic oscillations.