Existence of periodic travelling wave solutions of non-autonomous reaction–diffusion equations with lambda–omega type

Periodic travelling wave solutions of reaction–diffusion equations were studied by many authors. The λ – ω type reaction–diffusion system is a notable special model that admits explicit periodic travelling wave solutions and was introduced by Kopell and Howard in 1973. There are now similar systems which are investigated by means of autonomous dynamics. In contrast, there are few papers which are concerned with non-autonomous cases. For this reason, we apply Mawhin’s continuation theorem to derive the existence of periodic travelling wave solutions for non-autonomous λ – ω systems, and we describe the ‘disappearance’ of periodic travelling wave solutions under special situations. Our main result is also illustrated by examples.