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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.

34C25Periodic solutions of ODE
34A37Differential 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)
[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) · Zbl 0461.46001
[5] Hartman, P.: Ordinary differential equations. (1982) · Zbl 0476.34002
[6] Lakshmikantham, V.; Bainov, D. D.; Simeonov, P. S.: Theory of impulsive differential equations. (1989) · 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, No. 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)
[12] Tang, S.; Chen, L.: Impulsive semi-dynamical systems with applications in biological management (the doctor degree’s article). (2003)
[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, No. 4, 309-325 (2003) · Zbl 1046.92051