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On the existence and stability of a unique almost periodic solution of Schoener’s competition model with pure-delays and impulsive effects. (English) Zbl 1256.34074

The authors consider a 2D Schoener’s competition system with pure-delays, bounded almost periodic coefficients and impulsive effects. By using the results of [Y. Nakata and Y. Muroya, Nonlinear Anal., Real World Appl. 11, No. 1, 528–534 (2010; Zbl 1186.34119)] and a Lyapunov functional, they present a theorem on permanence, and an existence result about a unique uniformly asymptotically stable positive almost periodic solution.

MSC:

34K60 Qualitative investigation and simulation of models involving functional-differential equations
92D25 Population dynamics (general)
34K14 Almost and pseudo-almost periodic solutions to functional-differential equations
34K25 Asymptotic theory of functional-differential equations
34K20 Stability theory of functional-differential equations

Citations:

Zbl 1186.34119
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Full Text: DOI

References:

[1] Lu, Z.H.; Chen, L.S., Analysis on a periodic schoener model, Acta math sci, 12, Suppl, 105-109, (1992)
[2] Yuan, C.D.; Wang, C.H., Permanence and periodic solutions of the nonautonomous schoener’s competing system with diffusion, Biomathematics, 1, 2, 17-20, (1997), [in Chinese]
[3] Zhang, L.J.; Huo, H.F.; Chen, J.F., Asymptotic behavior of the nonautonomous competing system with feedback controls, J biomath, 16, 4, 405-410, (2001) · Zbl 1057.93505
[4] Liu, Q.M.; Xu, R., Periodic solutions of schoener’s competitive model with delays, J biomath, 19, 4, 385-394, (2004), [in Chinese] · Zbl 1115.92054
[5] Xiang, H.; Yan, K.M.; Wang, B.Y., Positive periodic solutions for discrete schoener’s competitive model, J Lanzhou univ technol, 31, 5, 125-128, (2005), [in Chinese]
[6] Liu, Q.M.; Xu, R.; Wang, W.G., Global asymptotic stability of schoener’s competitive model with delays, J biomath, 21, 1, 147-152, (2006), [in Chinese] · Zbl 1127.92311
[7] Li XP, Yang WS. Permanence of a discrete n-species Schoener competition system with time delays and feedback controls. Adv Differ Equations 2009; 2009. Article ID 515706, 10 p. · Zbl 1175.93090
[8] Wu, L.P.; Chen, F.D.; Li, Z., Permanence and global attractivity of a discrete schoener’s competition model with delays, Math comput model, 49, 1607-1617, (2009) · Zbl 1165.39302
[9] Bainov, D.D.; Simeonov, P.S., Impulsive differential equations: periodic solutions and applications, (1993), Longman Scientific and Technical · Zbl 0815.34001
[10] Lakshmikantham, V.; Bainov, D.D.; Simeonov, P.S., Theory of impulsive differential equations, (1989), World Scientific · Zbl 0719.34002
[11] Samoilenko, A.M.; Perestyuk, N.A., Impulsive differential equations, (1995), World Scientific Singapore · Zbl 0837.34003
[12] Jin, Z.; Han, M.A.; Li, G.H., The persistence in a lotka – volterra competition systems with impulsive, Chaos solitons fract, 24, 1105-1117, (2005) · Zbl 1081.34045
[13] Stamova, Ivanka M.; Stamov, Gani Tr., Asymptotic stability of impulsive neural networks with time-varying delay, Int J math manuscr, 1, 1, 158-168, (2007) · Zbl 1136.34332
[14] Li, Y.K.; Zhang, T.W., Existence of almost periodic solutions for Hopfield neural networks with continuously distributed delays and impulses, Electron J differ eqn, 2009, 152, 1-8, (2009) · Zbl 1186.34094
[15] Li, Y.K.; Zhang, T.W., Global exponential stability of fuzzy interval delayed neural networks with impulses on time scales, Int J neural syst, 19, 6, 449-456, (2009)
[16] Zhou, J.W.; Li, Y.K., Existence and multiplicity of solutions for some Dirichlet problems with impulsive effects, Nonlinear anal, 71, 2856-2865, (2009) · Zbl 1175.34035
[17] Li, Y.K.; Zhang, T.W., Existence and uniqueness of anti-periodic solution for a kind of forced Rayleigh equation with state dependent delay and impulses, Commun nonlinear sci numer simul, 15, 4076-4083, (2010) · Zbl 1222.34096
[18] Li, Y.K.; Zhang, T.W.; Xing, Z.W., The existence of nonzero almost periodic solution for cohen – grossberg neural networks with continuously distributed delays and impulses, Neurocomputing, 73, 3105-3113, (2010)
[19] Nakata, Y.; Muroya, Y., Permanence for nonautonomous lotka – volterra cooperative systems with delays, Nonlinear anal: RWA, 11, 528-534, (2010) · Zbl 1186.34119
[20] Zheng, Z.X., Theory of functional differential equations, (1994), Anhui Education Press
[21] He, C.Y., Almost periodic differential equations, (1992), Higher Education Publishing House Beijing, [in Chinese]
[22] Samoilenko, A.M.; Perestyuk, N.A., Differential equations with impulse effect, (1995), World Scientific Singapore · Zbl 0837.34003
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