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Periodicity and stability in a single-species model governed by impulsive differential equation. (English) Zbl 1243.34018
Summary: A periodic single-species model with periodic impulsive perturbations was investigated. By using Brouwer’s fixed point theorem and the Lyapunov function, sufficient conditions for the existence and global asymptotic stability of positive periodic solutions of the system were derived. Numerical simulations were presented to verify the feasibilities of our main results.

34A37Differential equations with impulses
34D23Global stability of ODE
92D25Population dynamics (general)
34C25Periodic solutions of ODE
Full Text: DOI
[1] Shi, R. Q.; Jiang, X. W.; Chen, L. S.: The effect of impulsive vaccination on an SIR epidemic model, Appl. math. Comput. 212, 305-311 (2009) · Zbl 1186.92040 · doi:10.1016/j.amc.2009.02.017
[2] Choisy, M.; Gugan, J. F.; Rohani, P.: Dynamics of infections diseases and pulse vaccination: teasing apart the embedded reasonance effects, Physica D 223, 26-35 (2006) · Zbl 1110.34031 · doi:10.1016/j.physd.2006.08.006
[3] Sun, S. L.; Chen, L. S.: Complex dynamics of a chemostat with variable yield and periodically impulsive perturbation on the substance, J. math. Chem. 43, 338-349 (2008) · Zbl 1135.92034 · doi:10.1007/s10910-006-9200-z
[4] Li, Z. X.; Wang, T. Y.; Chen, L. S.: Periodic solution of a chemostat model with beddington -- deanglis uptake function and impulsive state feedback control, J. theoret. Biol. 261, 23-32 (2009)
[5] Li, Z. X.; Chen, L. S.: Periodic solution of a turbidostat model with impulsive state feedback control, Nonlinear dynam. 58, 525-538 (2009) · Zbl 1183.92003 · doi:10.1007/s11071-009-9498-8
[6] Tang, S. Y.; Chen, L. S.: Density-dependent birth rate, birth pulses and their population dynamic consequences, J. math. Biol. 44, 185-199 (2002) · Zbl 0990.92033 · doi:10.1007/s002850100121
[7] Tang, S. Y.; Chen, L. S.: Multiple attractors in stage-structured population models with birth pulses, Bull. math. Biol. 65, 479-495 (2003)
[8] Liu, B.; Chen, L. S.: The periodic competing Lotka -- Volterra model with impulsive effect, Math. med. Biol. 21, 129-145 (2004) · Zbl 1055.92056 · doi:10.1093/imammb/21.2.129
[9] Liu, Z. J.; Tang, G. Y.; Qin, W. J.; Yang, Y.: Permanence in a periodic single species system subject to linear/constant impulsive perturbations, Math. method. Appl. sci. 33, 1516-1522 (2010) · Zbl 1200.34052 · doi:10.1002/mma.1271
[10] Liu, Z. J.; Wu, J. H.; Tan, R. H.: Permanence and extinction of an impulsive delay competitive Lotka-Volterra model with periodic coefficients, IMA J. Appl. math. 74, 559-573 (2009) · Zbl 1201.34131 · doi:10.1093/imamat/hxp007
[11] Liu, Z. J.; Tan, R. H.: Impulsive harvesting and stocking in a monod -- halsane functional response predator -- prey system, Chaos soliton. Fract. 34, 454-464 (2007) · Zbl 1127.92045 · doi:10.1016/j.chaos.2006.03.054
[12] Liu, Z. J.; Tan, R. H.; Chen, Y. P.: Modeling and analysis of a delayed competitive system with impulsive perturbations, Rocky mountain J. Math. 38, 1505-1524 (2008) · Zbl 1194.34093 · doi:10.1216/RMJ-2008-38-5-1505
[13] Liu, Z. J.; Hui, J.; Wu, J. H.: Permanence and partial extinction in an impulsive delay competitive system with the effect of toxic substances, J. math. Chem. 46, 1213-1231 (2009) · Zbl 1197.92046 · doi:10.1007/s10910-008-9513-1
[14] Tang, S. Y.; Xiao, Y. N.; Chen, L. S.; Cheke, R. A.: Integrated pest management models and their dynamical behaviour, Bull. math. Biol. 67, 115-135 (2005)
[15] Shi, R. Q.; Jiang, X. W.; Chen, L. S.: A predator-prey model with disease in the prey and two impulses for integrated pest management, Appl. math. Model. 33, 2248-2256 (2009) · Zbl 1185.34015 · doi:10.1016/j.apm.2008.06.001
[16] Lakmeche, A.; Arino, O.: Bifurcation of nontrivial periodic solutions of impulsive differential equations arising from chemotherapeutic treatments, Dyn. contin. Discrete impul. Syst. 7, 165-187 (2000) · Zbl 1011.34031
[17] Lakmeche, A.; Arino, O.: Nonlinear mathematical model of pulsed therapy of heterogeous tumors, Nonlinear anal. RWA 2, 455-465 (2001) · Zbl 0982.92016 · doi:10.1016/S1468-1218(01)00003-7
[18] Ludwig, D.; Jones, D. D.; Holling, C. S.: Qualitative analysis of insect outbreak systems:the spruce budworm and forest, J. animal ecol. 47, 315-332 (1978)
[19] Murray, J. D.: Mathematical biology I: An introduction, (2002) · Zbl 1006.92001
[20] Liu, X. N.; Chen, L. S.: Global dynamics of the periodic logistic system with periodic impulsive perturbations, J. math. Anal. appl. 289, 279-291 (2004) · Zbl 1054.34015 · doi:10.1016/j.jmaa.2003.09.058
[21] Smith, H. L.: Cooperative systems of differential equations with concave nonlinearities, Nonlinear anal. 10, 1037-1052 (1986) · Zbl 0612.34035 · doi:10.1016/0362-546X(86)90087-8