Title: Introduction to Delay Models and Their Wave Solutions,
Abstract: In this paper, a brief review of delay population models and their
applications in ecology is provided. The inclusion of diffusion and nonlocality
terms in delay models has given more capabilities to these models enabling them
to capture several ecological phenomena such as the Allee effect, waves of
invasive species and spatio-temporal competitions of interacting species.
Moreover, recent advances in the studies of traveling and stationary wave
solutions of delay models are outlined. In particular, the existence of
stationary and traveling wave solutions of delay models, stability of wave
solutions, formation of wavefronts in the special domain, and possible outcomes
of delay models are discussed.