In this paper, we study traveling wave solutions of the chemotaxis systems begin{equation} begin{cases} u_{t}=Delta u -chi_1 abla( u abla v_1)+chi_2 abla(u abla v_2 )+ u(a -b u), qquad xinmathbb{R} taupartial_tv_1=(Delta- lambda_1 I)v_1+ mu_1 u, qquad xinmathbb{R}, taupartial v_2=(Delta- lambda_2 I)v_2+ mu_2 u, qquad xinmathbb{R}, end{cases} (0.1) end{equation} where $tau>0,chi_{i}> 0,lambda_i> 0, mu_i>0$ ($i=1,2$) and $ a>0, b> 0$ are constants, and $N$ is a positive integer. Under some appropriate conditions on the parameters, we show that there exist two positive constant $ 0<c^{*}(tau,chi_1,mu_1,lambda_1,chi_2,mu_2,lambda_2)<c^{**}(tau,chi_1,mu_1,lambda_1,chi_2,mu_2,lambda_2)$ such that for every $c^{*}(tau,chi_1,mu_1,lambda_1,chi_2,mu_2,lambda_2)leq c<c^{**}(tau,chi_1,mu_1,lambda_1,chi_2,mu_2,lambda_2)$, $(0.1)$ has a traveling wave solution $(u,v_1,v_2)(x,t)=(U,V_1,V_2)(x-ct)$ connecting $(frac{a}{b},frac{amu_1}{blambda_1},frac{amu_2}{blambda_2})$ and $(0,0,0)$ satisfying $$ lim_{zto infty}frac{U(z)}{e^{-mu z}}=1, $$ where $muin (0,sqrt a)$ is such that $c=c_mu:=mu+frac{a}{mu}$. Moreover, $$ lim_{(chi_1,chi_2)to (0^+,0^+))}c^{**}(tau,chi_1,mu_1,lambda_1,chi_2,mu_2,lambda_2)=infty$$ and $$lim_{(chi_1,chi_2)to (0^+,0^+))}c^{*}(tau,chi_1,mu_1,lambda_1,chi_2,mu_2,lambda_2)= c_{tilde{mu}^*}, $$ where $tilde{mu}^*={min{sqrt{a}, sqrt{frac{lambda_1+tau a}{(1-tau)_{+}}},sqrt{frac{lambda_2+tau a}{(1-tau)_{+}}}}}$. We also show that $(0.1)$ has no traveling wave solution connecting $(frac{a}{b},frac{amu_1}{blambda_1},frac{amu_2}{blambda_2})$ and $(0,0,0)$ with speed $c<2sqrt{a}$.
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