Positive almost periodic solutions for state-dependent delay Lotka-Volterra competition systems

In this article, using Mawhin's continuation theorem of coincidence degree theory, we obtain sufficient conditions for the existence of positive almost periodic solutions for the system of equations $$ dot{u}_i(t)=u_i(t)Big[r_i(t)-a_{ii}(t)u_i(t) -sum_{j=1, j eq i}^na_{ij}(t)u_jig(t- au_j(t,u_1(t), dots,u_n(t))ig)Big], $$ where $r_i,a_{ii}>0$, $a_{ij}geq0(j eq i$, $i,j=1,2,dots,n)$ are almost periodic functions, $ au_iin C(mathbb{R}^{n+1},mathbb{R})$, and $ au_i(i=1,2,dots,n)$ are almost periodic in $t$ uniformly for $(u_1,dots,u_n)^Tinmathbb{R}^n$. An example and its simulation figure illustrate our results.