Global attractivity of positive periodic solution of a delayed Nicholson model with nonlinear density-dependent mortality term

• Main Authors: Thai Doan, Le Van Hien, Anh Trinh
• Format: Article
• Language: English
• Published: University of Szeged 2019-02-01
• Series: Electronic Journal of Qualitative Theory of Differential Equations
• Subjects: nicholson's blowflies model; positive periodic solution; attractivity; time-varying delays; nonlinear density-dependent mortality
• Online Access: http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1&paramtipus_ertek=publication&param_ertek=6563

This paper is concerned with the existence, uniqueness and global attractivity of positive periodic solution of a delayed Nicholson's blowflies model with nonlinear density-dependent mortality rate. By some comparison techniques via differential inequalities, we first establish sufficient conditions for the global uniform permanence and dissipativity of the model. We then utilize an extended version of the Lyapunov functional method to show the existence and global attractivity of a unique positive periodic solution of the underlying model. An application to the model with constant coefficients is also presented. Two numerical examples with simulations are given to illustrate the efficacy of the obtained results.