Conditional Ulam stability and its application to the logistic model

M. Onitsuka

This study deals with conditional Ulam stability for the logistic equation $\frac{dx}{dt} = x(a+bx)$ for $t\ge 0$, where $a \neq 0 \neq b$.
The core of this study is establishing conditional Ulam stability for the equation $\frac{dx}{dt} = x(x-1)$ for $t\ge 0$.
The main theorem can be obtained by combining a result obtained by Popa, Ra\c{s}a and Viorel [Appl. Math. Lett. 85 (2018), pp. 64--69] with a result of this study.
Finally, the obtained result is applied to the logistic model $\frac{dP}{dt}=r\left(1-\frac{P}{K}\right)P$.

Applied Mathematics Letters

122

107565

1

7

https://doi.org/10.1016/j.aml.2021.107565