Dynamic Analysis of a Model for Spruce Budworm Populations with Delay

Abstract

A class of delayed spruce budworm population model is considered. Compared with previous studies, both autonomous and nonautonomous delayed spruce budworm population models are considered. By using the inequality techniques, continuation theorem, and the construction of suitable Lyapunov functional, we establish a set of easily verifiable sufficient conditions on the permanence, existence, and global attractivity of positive periodic solutions for the considered system. Finally, an example and its numerical simulation are given to illustrate our main results.