Dynamics in a Nonautonomous Nicholson-Type Delay System

Abstract

A kind of Nicholson-type delay system is considered. Several conditions on the ultimate boundedness, extinction, permanence, periodic solution, and global attractivity of the system are established by employing the inequality techniques and comparison method and constructing suitable Lyapunov functional.

Dynamics in a Competitive Nicholson’s Blowflies Model with Continuous Time Delays

“…By constructing appropriate Lyapunov functions and several useful inequalities, several criteria for the permanence, extinction, periodic solutions, and global attractiveness of the system were obtained. From this study, we found that the main results and system (6) can be seen as supplements and extensions of the previously results and systems [1][2][3][4][5][6][7][8][9][10][11][12].…”

“…Some results on the stability and attractiveness of equilibrium points were obtained for system (5). It can be found that system (5) and the considered systems in [7,8] are autonomous, and the time delays are discrete. However, in the real world, nonautonomous variable time-delayed differential equations can better reflect the real ecosystem situation.…”