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- W4323338889 abstract "<abstract><p>In this paper, we study the following initial-boundary value problem of a three species predator-prey system with prey-taxis which describes the indirect prey interactions through a shared predator, i.e.,</p> <p><disp-formula> <label/> <tex-math id=FE1> begin{document}$ begin{align*} begin{cases} u_t = dDelta u+u(1-u)- frac{a_1uw}{1+a_2u+a_3v}, & ; mbox{in} Omega, t>0, v_t = eta dDelta v+rv(1-v)- frac{a_4vw}{1+a_2u+a_3v}, & ; mbox{in} Omega, t>0, w_t = nablacdot(nabla w-chi_1 wnabla u-chi_2 wnabla v) -mu w+ frac{a_5uw}{1+a_2u+a_3v}+frac{a_6vw}{1+a_2u+a_3v}, & mbox{in} Omega, t>0, label{II} end{cases} end{align*} $end{document} </tex-math></disp-formula></p> <p>under homogeneous Neumann boundary conditions in a bounded domain $ Omegasubset mathbb{R}^n (n geqslant 1) $ with smooth boundary, where the parameters $ d, eta, r, mu, chi_1, chi_2, a_i > 0, i = 1, ldots, 6. $ We first establish the global existence and uniform-in-time boundedness of solutions in any dimensional bounded domain under certain conditions. Moreover, we prove the global stability of the prey-only state and coexistence steady state by using Lyapunov functionals and LaSalle's invariance principle.</p></abstract>" @default.
- W4323338889 created "2023-03-08" @default.
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- W4323338889 date "2023-01-01" @default.
- W4323338889 modified "2023-09-30" @default.
- W4323338889 title "Global existence and stability of three species predator-prey system with prey-taxis" @default.
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- W4323338889 doi "https://doi.org/10.3934/mbe.2023371" @default.
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