Positive Periodic Solutions for a Neutral Impulsive Delay Competition System

Authors: Daiming Wang

Abstract:

In this paper, a neutral impulsive competition system with distributed delays is studied by using Mawhin-s coincidence degree theory and the mean value theorem of differential calculus. Sufficient conditions on the existence of positive periodic solution of the system are obtained.

Keywords: Neutral impulsive delay system, competitive system, coincidence degree, periodic solution, existence.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1080416

References:

[1] Y. Li, Positive periodic solution for neutral delay model, Acta Math. Sinica 39 (1996) 789-795 (in Chinese).
[2] Y. Li, Periodic solution of a periodic neutral delay equation, J. Math. Anal. Appl. 214 (1997) 11-21.
[3] K. Gopalsamy, Stability and Oscillations in Delay Differential Equations of Population Dynamics, Kluwer Academic, Boston, 1992.
[4] Y. Kuang, On neutral delay two species Lotka-Volterra competitive system, J. Austral. Math. Soc. Ser. B 32 (1991) 311-326.
[5] Y. Zhu, Periodic solutions for a higher order nonlinear neutral functional differential equation. Inter. J. Comp. Math. Sci., 5 (2011) 8-12.
[6] Y. Li, On a periodic neutral delay Lotka-Volterra system, Nonlinear Anal. 39 (2000) 767-778.
[7] Z. Liu, Positive periodic solution for a neutral delay competitive system, J. Math. Anal. Appl. 293 (2004) 181-189.
[8] X. Ding, S. Cheng, Positive periodic solution for a nonautonomous logistic model with linear feedback regulation, Appl. Math. J. Chinese Univ. Ser. B, 21 (2006) 302-312.
[9] X. Ding, Periodicity in a delayded semi-ratio-dependent predator-prey system, Appl. Math. J. Chinese Univ. Ser. B, 20 (2005) 151-158.
[10] Y. Li, W. Xing, L. Lu, Existence and global exponential stability of periodic solution of a class of neural networks with impulses, Chaos, Solitions and Fractals (2006) 437-445.
[11] H. Huo, Existence of positive periodic solution for a neutral delay Lotka-Volterra system with impulses, Computers and Mathematics with Applications 48 (2004) 1833-1846.
[12] H. Huo, W. Li, Existence of positive periodic solution of a neutral impulsive delay predator-prey system, Applied Mathematics and Computation 185 (2007) 499-507.
[13] D. Wang, C. Feng, Three positive periodic solutions to a kind of Impulsive Differential Equations with delay, Journal of Jilin University, Science Edition, 3 (2011) 391-396.
[14] Z. Liu, L. Chen, Periodic solution of a two-species competitive system with toxicant and birth pulse, Chaos, Solitons and Fractals 32 (2007) 1703-1712.
[15] Y. Li, Z. Xing, Existence and global exponential stability of periodic solutions of CNNs with impulses, Chaos, Solitons and Fractals 33 (2007) 1686-1693.
[16] R. Gaines, J. Mawhin, Coincidence Degree and Nonlinear Differential Equations, Springer-Verlag, Berlin, 1977.