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Boundedness and asymptotic stability in a twospecies chemotaxiscompetition model with signaldependent sensitivity
Department of Mathematics, Tokyo University of Science, 13 Kagurazaka, Shinjukuku, Tokyo 1628601, Japan 
$\left\{ {\begin{array}{*{20}{l}}{{u_t} = {d_1}\Delta u  \nabla \cdot (u{\chi _1}(w)\nabla w) + {\mu _1}u(1  u  {a_1}v)}&{;{\rm{in}}\;\Omega \times (0,\infty ),}\\{{v_t} = {d_2}\Delta v  \nabla \cdot (v{\chi _2}(w)\nabla w) + {\mu _2}v(1  {a_2}u  v)}&{;{\rm{in}}\;\Omega \times (0,\infty ),}\\{{w_t} = {d_3}\Delta w + h(u,v,w)}&{;{\rm{in}}\;\Omega \times (0,\infty ),}\end{array}} \right.$ 
$\Omega$ 
$\mathbb{R}^n$ 
$\partial \Omega$ 
$n\in \mathbb{N}$ 
$h$ 
$\chi_i$ 
$\chi_i(w)=\chi_i$ 
$\mu_1, \mu_2$ 
$\mu_1, \mu_2$ 
References:
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References:
[1] 
Harumi Hattori, Aesha Lagha. Global existence and decay rates of the solutions for a chemotaxis system with LotkaVolterra type model for chemoattractant and repellent. Discrete and Continuous Dynamical Systems, 2021, 41 (11) : 51415164. doi: 10.3934/dcds.2021071 
[2] 
Yukio KanOn. Global bifurcation structure of stationary solutions for a LotkaVolterra competition model. Discrete and Continuous Dynamical Systems, 2002, 8 (1) : 147162. doi: 10.3934/dcds.2002.8.147 
[3] 
De Tang. Dynamical behavior for a LotkaVolterra weak competition system in advective homogeneous environment. Discrete and Continuous Dynamical Systems  B, 2019, 24 (9) : 49134928. doi: 10.3934/dcdsb.2019037 
[4] 
Marco Di Francesco, Alexander Lorz, Peter A. Markowich. Chemotaxisfluid coupled model for swimming bacteria with nonlinear diffusion: Global existence and asymptotic behavior. Discrete and Continuous Dynamical Systems, 2010, 28 (4) : 14371453. doi: 10.3934/dcds.2010.28.1437 
[5] 
Mihaela Negreanu. Global existence and asymptotic behavior of solutions to a chemotaxis system with chemicals and preypredator terms. Discrete and Continuous Dynamical Systems  B, 2020, 25 (9) : 33353356. doi: 10.3934/dcdsb.2020064 
[6] 
ZhiCheng Wang, HuiLing Niu, Shigui Ruan. On the existence of axisymmetric traveling fronts in LotkaVolterra competitiondiffusion systems in ℝ^{3}. Discrete and Continuous Dynamical Systems  B, 2017, 22 (3) : 11111144. doi: 10.3934/dcdsb.2017055 
[7] 
Yukio KanOn. Bifurcation structures of positive stationary solutions for a LotkaVolterra competition model with diffusion II: Global structure. Discrete and Continuous Dynamical Systems, 2006, 14 (1) : 135148. doi: 10.3934/dcds.2006.14.135 
[8] 
Qi Wang. Some global dynamics of a LotkaVolterra competitiondiffusionadvection system. Communications on Pure and Applied Analysis, 2020, 19 (6) : 32453255. doi: 10.3934/cpaa.2020142 
[9] 
Qian Guo, Xiaoqing He, WeiMing Ni. Global dynamics of a general LotkaVolterra competitiondiffusion system in heterogeneous environments. Discrete and Continuous Dynamical Systems, 2020, 40 (11) : 65476573. doi: 10.3934/dcds.2020290 
[10] 
Pan Zheng. Asymptotic stability in a chemotaxiscompetition system with indirect signal production. Discrete and Continuous Dynamical Systems, 2021, 41 (3) : 12071223. doi: 10.3934/dcds.2020315 
[11] 
Tobias Black. Global existence and asymptotic stability in a competitive twospecies chemotaxis system with two signals. Discrete and Continuous Dynamical Systems  B, 2017, 22 (4) : 12531272. doi: 10.3934/dcdsb.2017061 
[12] 
S. Nakaoka, Y. Saito, Y. Takeuchi. Stability, delay, and chaotic behavior in a LotkaVolterra predatorprey system. Mathematical Biosciences & Engineering, 2006, 3 (1) : 173187. doi: 10.3934/mbe.2006.3.173 
[13] 
Yasuhisa Saito. A global stability result for an Nspecies LotkaVolterra food chain system with distributed time delays. Conference Publications, 2003, 2003 (Special) : 771777. doi: 10.3934/proc.2003.2003.771 
[14] 
GuoBao Zhang, Ruyun Ma, XueShi Li. Traveling waves of a LotkaVolterra strong competition system with nonlocal dispersal. Discrete and Continuous Dynamical Systems  B, 2018, 23 (2) : 587608. doi: 10.3934/dcdsb.2018035 
[15] 
LihIng W. Roeger, Razvan Gelca. Dynamically consistent discretetime LotkaVolterra competition models. Conference Publications, 2009, 2009 (Special) : 650658. doi: 10.3934/proc.2009.2009.650 
[16] 
Yuan Lou, WeiMing Ni, Shoji Yotsutani. On a limiting system in the LotkaVolterra competition with crossdiffusion. Discrete and Continuous Dynamical Systems, 2004, 10 (1&2) : 435458. doi: 10.3934/dcds.2004.10.435 
[17] 
Qi Wang, Yang Song, Lingjie Shao. Boundedness and persistence of populations in advective LotkaVolterra competition system. Discrete and Continuous Dynamical Systems  B, 2018, 23 (6) : 22452263. doi: 10.3934/dcdsb.2018195 
[18] 
Yuan Lou, Dongmei Xiao, Peng Zhou. Qualitative analysis for a LotkaVolterra competition system in advective homogeneous environment. Discrete and Continuous Dynamical Systems, 2016, 36 (2) : 953969. doi: 10.3934/dcds.2016.36.953 
[19] 
BangSheng Han, ZhiCheng Wang, Zengji Du. Traveling waves for nonlocal LotkaVolterra competition systems. Discrete and Continuous Dynamical Systems  B, 2020, 25 (5) : 19591983. doi: 10.3934/dcdsb.2020011 
[20] 
Dan Wei, Shangjiang Guo. Qualitative analysis of a LotkaVolterra competitiondiffusionadvection system. Discrete and Continuous Dynamical Systems  B, 2021, 26 (5) : 25992623. doi: 10.3934/dcdsb.2020197 
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