Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 91, pp. 1-10.
Title: Positive almost periodic solutions for state-dependent
delay Lotka-Volterra competition systems
Authors: Yongkun Li (Yunnan Univ., China)
Chao Wang (Yunnan Univ., China)
Abstract:
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
$$
\dot{u}_i(t)=u_i(t)\Big[r_i(t)-a_{ii}(t)u_i(t)
-\sum_{j=1, j\neq i}^na_{ij}(t)u_j\big(t-\tau_j(t,u_1(t),
\dots,u_n(t))\big)\Big],
$$
where $r_i,a_{ii}>0$, $a_{ij}\geq0(j\neq i$, $i,j=1,2,\dots,n)$ are
almost periodic functions, $\tau_i\in C(\mathbb{R}^{n+1},\mathbb{R})$,
and $\tau_i(i=1,2,\dots,n)$ are almost periodic in $t$ uniformly for
$(u_1,\dots,u_n)^T\in\mathbb{R}^n$. An example and its
simulation figure illustrate our results.
Submitted April 12, 2012. Published June 07, 2012.
Math Subject Classifications: 34K14, 92D25.
Key Words: Lotka-Volterra competition system; almost periodic solutions;
coincidence degree; state dependent delays.