This paper extends the \(\theta \) -logistic model to a more realistic nonautonomous framework that provides a wider perspective. This perspective grants all parameters the flexibility to vary with time. In this context, we show; from a mathematical point of view, the positivity and the continuation of solutions. In addition, we explore conditions under which the asymptotic behavior of the population density is in accordance with (or contrary to) that of time-varying carrying capacity. Accordingly, contributions are added to overcome the so-called Levins’ paradox and to clarify the case when extinction occurs even if the time-varying carrying capacity is unbounded. Some mathematical notions like origin attractivity and asymptotic stability are also discussed.
