Dynamics in a Delayed Competition System on a Weighted Network

In this paper, we study the stability of positive steady states in a delayed competition system on a weighted network, which does not satisfy the comparison principle appealing to classical competitive systems. By introducing some auxiliary equations and constructing proper contracting rectangles, we present some sufficient conditions on the stability of the unique positive steady state. Moreover, some numerical examples are given to explore the complex dynamics of this nonmonotone model, which implies the nontrivial roles of weights and time delays