Description

• Title:
  Coexistence states of diffusive predator-prey systems with preys competition and predator saturation
• Creator:
  Zhou, Jun
• Description:
  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:-\Delta u=u\bigg(a_1-u-b_{12}v-\frac{c_1w}{(1+\alpha_1u)(1+\beta_1w)}\bigg) & {\rm in}\ \Omega, -\Delta v=v\bigg(a_2-b_{21}u-v-\frac{c_2w}{(1+\alpha_2v)(1+\beta_2w)}\bigg) &{\rm in}\ \Omega, -\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, k_1\partial_\nu u+u=k_2\partial_\nu v+v=k_3\partial_\nu w+w=0 & {\rm on}\ \partial\Omega, where $k_i\geq 0$ $(i=1,2,3)$ and all the other parameters are positive, $\nu$ is the outward unit rector on $\partial\Omega$, $u$ and $v$ are densities of the competing preys, $w$ is the density of the predator.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2015 Topological Methods in Nonlinear Analysis
• Date:
  2015.06.01
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 45, No 2 (June 2015); 509 - 550;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.025/7457
• Subject:
  Coexistence;
  Predator-prey model;
  fix point index;
  extinction;
  permanence;
  global attractor;
  stability;
  35J60;
  35K55;
  35K57;
  92D25
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2015.025
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other