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Existence of periodic solution of order one of planar impulsive autonomous system. (English) Zbl 1088.34040
The authors investigate the state-dependent impulsive differential equations wich have no explicit solution. Sufficient conditions for the existence of a periodic solution of order one for such systems are proved.

34C25 Periodic solutions to ordinary differential equations
34A37 Ordinary differential equations with impulses
Full Text: DOI
[1] Angelova, J.; Dishliev, A., Optimization problems for one-impulsive models from population dynamics, Nonlinear anal., 39, 483-497, (2000) · Zbl 0942.34010
[2] Chen, L.; Song, X.; Lu, Z., Mathematical models and methods in ecology, (2003), Sichuan Science and technology Chendu, China, (in Chinese)
[3] Corless, R.M.; Gonnet, G.H.; Hare, D.E.G.; Jeffrey, D.J.; Knuth, D.E., On the Lambert W function, Adv. comput. math., 5, 329-359, (1996) · Zbl 0863.65008
[4] Griffel, D.H., Applied functional anaylsis, (1981), Ellis Horwood Ltd Chichester, England · Zbl 0461.46001
[5] Hartman, P., Ordinary differential equations, (1982), Birkhäuser Boston · Zbl 0125.32102
[6] Lakshmikantham, V.; Bainov, D.D.; Simeonov, P.S., Theory of impulsive differential equations, (1989), World Scientific Singapore · Zbl 0719.34002
[7] X. Liu, Stability results for impulsive differential systems with applications to population growth models, Dynamics and Stability of Systems, vol. 9(2), 1994, pp. 163-174. · Zbl 0808.34056
[8] Liu, X.; Chen, L., Complex dynamics of Holling type II lotka – volterra predator – prey system with impulsive perturbations on the predator, Chaos soliton. fractal., 16, 311-320, (2003) · Zbl 1085.34529
[9] Liu, X.; Chen, L., Global dynamics of the periodic logistic system with periodic impulsive perturbations, J. math. anal. appl., 289, 279-291, (2004) · Zbl 1054.34015
[10] Liu, B.; Chen, L.; Zhang, Y., The effects of impulsive toxicant input on a population in a polluted environment, J. biol. syst., 11, 3, 265-274, (2003) · Zbl 1041.92044
[11] Tang, S.; Chen, L., Multiple attractors in stage-structured population models with birth pulses, Bull. math. biol., 65, 479-595, (2003) · Zbl 1334.92371
[12] Tang, S.; Chen, L., Impulsive semi-dynamical systems with applications in biological management (the doctor Degree’s article), (2003), Chinese Academy of Sciences, (in Chinese)
[13] Zhang, Y.; Liu, B.; Chen, L., Extinction and permanence of a two-prey one-predator system with impulsive effect, IMA J. math. med. biol., 20, 4, 309-325, (2003) · Zbl 1046.92051
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