Existence and stability of periodic solution of a stage‐structured model with state‐dependent impulsive effects |
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Authors: | Linfei Nie Zhidong Teng Lin Hu |
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Affiliation: | College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, People's Republic of China |
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Abstract: | 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. |
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Keywords: | impulsive differential equations stage structure order‐k periodic solution orbitally asymptotically stable |
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