Forced waves and their asymptotics in a Lotka–Volterra cooperative model under climate change

Abstract

The existence and asymptotics of forced traveling wave front in a Lotka–Volterra cooperative system under climate change are concerned in this paper. By constructing appropriate upper and lower solutions combined with the monotone iteration scheme, we show that for any given positive speed of the shifting habitat edge, there exists a nondecreasing wave front with the speed consistent with the habitat shifting speed, which indicates that no matter how moderate of the habitat shifts, two species will still be driven to extinction as the mutualistic effects exist but weak. Numerical simulations are also given to illustrate our results.