Coexistence states of diffusive predator-prey systems with preys competition and predator saturation

Jun Zhou

DOI: http://dx.doi.org/10.12775/TMNA.2015.025

Abstract


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.


Keywords


Coexistence; Predator-prey model; fix point index;extinction; permanence; global attractor; stability

Full Text:

Full Text

Refbacks

  • There are currently no refbacks.

Partnerzy platformy czasopism