@article{Zhou_2015, title={Coexistence states of diffusive predator-prey systems with preys competition and predator saturation}, volume={45}, url={https://apcz.umk.pl/TMNA/article/view/TMNA.2015.025}, DOI={10.12775/TMNA.2015.025}, abstractNote={<p>In this paper, we study the existence, stability, permanence, and global attractor of coexistence states (i.e. the densities of all the species are positive in $\Omega$) to the following diffusive two-competing-prey and one-predator systems with preys competition and predator saturation:</p><p><span>-\Delta u=u\bigg(a_1-u-b_{12}v-\frac{c_1w}{(1+\alpha_1u)(1+\beta_1w)}\bigg) & {\rm in}\ \Omega,<br /> -\Delta v=v\bigg(a_2-b_{21}u-v-\frac{c_2w}{(1+\alpha_2v)(1+\beta_2w)}\bigg) &{\rm in}\ \Omega,<br /> -\Delta w=w\bigg(\frac{e_1u}{(1+\alpha_1u)(1+\beta_1w)}+\frac{e_2v}{(1+\alpha_2v)(1+\beta_2w)}-d\bigg) &{\rm in}\ \Omega,<br /> k_1\partial_ u u+u=k_2\partial_ u v+v=k_3\partial_ u w+w=0 & {\rm on}\ \partial\Omega, </span></p><p>where $k_i\geq 0$ $(i=1,2,3)$ and all the other parameters are positive, $ u$ is the outward unit rector on $\partial\Omega$, $u$ and $v$ are densities of the competing preys, $w$ is the density of the predator.</p>}, number={2}, journal={Topological Methods in Nonlinear Analysis}, author={Zhou, Jun}, year={2015}, month={Jun.}, pages={509–550} }