Long-time behavior of a size-structured population model with diffusion and delayed birth process

<p style='text-indent:20px;'>This work focuses on the long time behavior for a size-dependent population system with diffusion and Riker type birth function. Some dynamical properties of the considered system is investigated by using <inline-formula><tex-math id="M1">\begin{document}$ C_0 $\end{document}</tex-math></inline-formula>-semigroup theory and spectral analysis arguments. Some sufficient conditions are obtained respectively for asymptotical stability, asynchronous exponential growth at the null equilibrium as well as Hopf bifurcation occurring at the positive steady state of the system. In the end several examples and their simulations are also provided to illustrate the achieved results.</p>