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A stage structure pest management model with impulsive state feedback control. (English) Zbl 1353.91032
Summary: A stage structure pest management model with impulsive state feedback control is investigated. We get the sufficient condition for the existence of the order-1 periodic solution by differential equation geometry theory and successor function. Further, we obtain a new judgement method for the stability of the order-1 periodic solution of the semi-continuous systems by referencing the stability analysis for limit cycles of continuous systems, which is different from the previous method of analog of PoincarĂ¨ criterion. Finally, we analyze numerically the theoretical results obtained.

##### MSC:
 91B76 Environmental economics (natural resource models, harvesting, pollution, etc.) 93B52 Feedback control
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##### References:
 [1] Song, X.; Chen, L., Global asymptotic stability of a two species competitive system with stage structure and harvesting, Commun Nonlinear Sci Numer Simul, 6, 81-87, (2001) · Zbl 0994.34066 [2] Xiao, Y.; Chen, L., Analysis of a SIS epidemic model with stage structure and a delay, Commun Nonlinear Sci Numer Simul, 6, 35-39, (2001) · Zbl 1040.34096 [3] Pang, G.; Wang, F.; Chen, L., Extinction and permanence in delayed stage-structure predator-prey system with impulsive effects, Chaos Solitons Fract, 39, 2216-2224, (2009) · Zbl 1197.34158 [4] Huang, M.; Duan, G.; Song, X., A predator-prey system with impulsive state feedback control, Math Appl, 25, 3, 661-666, (2012) [5] Zhao, Z.; Wang, T.; Chen, L., Dynamic analysis of a turbidostat model with the feedback control, Commun Nonlinear Sci Numer Simul, 15, 1028-1035, (2010) · Zbl 1221.93052 [6] Wang, T.; Chen, L., Nonlinear analysis of a microbial pesticide model with impulsive state feedback control, Nonlinear Dyn, 65, 1-10, (2011) · Zbl 1235.93108 [7] Huang, M.; Song, X.; Guo, H., Study on species cooperative systems with impulsive state feedback control, J Syst Sci Math Sci, 32, 3, 265-276, (2012) · Zbl 1274.34143 [8] Wei, C.; Chen, L., A Leslie-gower pest management model with impulsive state feedback control, Int J Biomath, 27, 4, 621-628, (2012) · Zbl 1289.92087 [9] Bainov, D.; Simeonov, P., Impulsive differential equations: periodic solutions and applications, (1993), Longman Scientific and Technical New York · Zbl 0815.34001 [10] Fu J, Wang Y. The mathematical study of pest management strategy. Discrete Dyn Nat Soc, in press. http://dx.doi.org/10.1155/2012/251942. [11] Wei C, Zhang S, Chen L. Impulsive state feedback control of cheese whey fermentation for single-cell protein production. J Appl Math, in press. http://dx.doi.org/10.1155/2013/354095. [12] Chen, L., Pest control and geometric theory of semi-continuous dynamical system, J Beihua Univ (Nat Sci), 12, 1, 1-9, (2011) [13] Ma, Z.; Zhou, Y., Postgraduate education series: ordinary differential equation qualitative and stability theory, (2013), Science Press Beijing [14] Chen, L., Theory and application of semi-continuous dynamical system, J Yulin Normal Univ (Nat Sci), 34, 2, 1-10, (2013) [15] Diliberto, S. P., Contributions to the theory of nonlinear oscillations, I, (1950), Princeton University Press Princeton
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