Asymptotic behavior of solutions to a system of differential equations with state-dependent delays (Q1019791)

Editorial remark: This article has been retracted at the request of the Journal Editor: ``The article is very similar to the following papers: (1) ``Asymptotic behavior of solutions to a differential equation with state-dependent delay'' by \textit{L. Peng}, Comput. Math. Appl. 57, No. 9, 1511--1514 (2009; Zbl 1186.34107) (2) `Asymptotic constancy for a differential equation with multiple state-dependent delays' by \textit{W. Wang, G. Yue, Ch. Ou}, J. Comput. Appl. Math. 233, No. 2, 356--360 (2009; Zbl 1206.34097). All these articles were written using the same Latex file, treating very similar problems in exactly the same way. The authors of the papers knew about the similarity between the papers, but did not make any reference to each other, and therefore violated the Ethical Rules of Publishing, at the time the papers were submitted for publication. The scientific community takes a very strong view on this matter and apologies are offered to readers of the journal that this was not detected during the submission process.'' Review: It is shown that every bounded solution of the following system \[ \begin{aligned} x_1'(t)=-F(x_1(t))+G(x_2(t-r_2),\quad r_2=r_2(x_2(t-\delta_2));\\ x_2'(t)=-F(x_2(t))+G(x_1(t-r_1),\quad r_1=r_1(x_1(t-\delta_1))\end{aligned} \] is convergent to a constant solution. The main technique is based on a monotonicity argument.