Dynamic analysis of an impulsive differential equation with time-varying delays
Tóm tắt
Từ khóa
Tài liệu tham khảo
J.O. Alzabut, T. Abdeljawad: On existence of a globally attractive periodic solution of impulsive delay logarithmic population model. Appl. Math. Comput. 198 (2008), 463–469.
X. Ding, J. Jiang: Periodicity in a generalized semi-ratio-dependent predator-prey system with time delays and impulses. J. Math. Anal. Appl. 360 (2009), 223–234.
R.E. Gaines, J. L. Mawhin: Coincidence Degree, and Nonlinear Differential Equations. Lecture Notes in Mathematics 568, Springer, Berlin, 1977.
K. Gopalsamy: Stability and Oscillations in Delay Differential Equations of Population Dynamics. Mathematics and its Applications 74, Kluwer Academic Publishers, Dordrecht, 1992.
M. He, F. Chen: Dynamic behaviors of the impulsive periodic multi-species predator-prey system. Comput. Math. Appl. 57 (2009), 248–256.
Y. Kuang: Delay Differential Equations: with Applications in Population Dynamics. Mathematics in Science and Engineering 191, Academic Press, Boston, 1993.
V. Lakshmikantham, D.D. Bajnov, P. S. Simeonov: Theory of Impulsive Differential Equations. Series in Modern Applied Mathematics 6, World Scientific, Singapore, 1989.
X. Liu, Y. Takeuchi: Periodicity and global dynamics of an impulsive delay Lasota-Wazewska model. J. Math. Anal. Appl. 327 (2007), 326–341.
V.G. Nazarenko: Influence of delay on auto oscillation in cell population. Biofisika 21 (1976), 352–356.
S.H. Saker, J.O. Alzabut: Existence of periodic solutions, global attractivity and oscillation of impulsive delay population model. Nonlinear Anal., Real World Appl. 8 (2007), 1029–1039.
Y. Shao, B. Dai, Z. Luo: The dynamics of an impulsive one-prey multi-predators system with delay and Holling-type II functional response. Appl. Math. Comput. 217 (2010), 2414–2424.
Y. Shao, Y. Li, C. Xu: Periodic solutions for a class of nonautonomous differential system with impulses and time-varying delays. Acta Appl. Math. 115 (2011), 105–121.