Premium
Existence and stability of periodic solution of a stage‐structured model with state‐dependent impulsive effects
Author(s) -
Nie Linfei,
Teng Zhidong,
Hu Lin
Publication year - 2011
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1468
Subject(s) - mathematics , stability (learning theory) , state (computer science) , control theory (sociology) , population model , state dependent , order (exchange) , population , control (management) , mathematical economics , computer science , algorithm , demography , finance , machine learning , artificial intelligence , sociology , economics
A single population growth model with stage‐structured and state‐dependent impulsive control is proposed. By using the Poincar'e map and the analogue of Poincaré's criterion, we prove the existence and the stability of positive order‐1 or order‐2 periodic solution. Moreover, we show that there is no periodic solution with order greater than or equal to three. Numerical results are carried out to illustrate the feasibility of our main results and the superiority of state feedback control strategy is also discussed. Copyright © 2011 John Wiley & Sons, Ltd.