Abstract
This paper studies the minimal wave speed of traveling wave solutions in a delayed competitive model, which describes the synchronous invasion of all competitors. Here, the traveling wave solutions connect the trivial steady state with the positive steady state. We confirm the existence and nonexistence of traveling wave solutions for all positive wave speeds, which gives the minimal wave speed and decaying behavior of traveling wave solutions. Our main recipes are comparison principle, upper and lower solutions, contracting rectangles and asymptotic spreading. Moreover, our proof can be extended to Lotka-Volterra type systems to complete earlier conclusions.
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