Periodic Oscillations in a Delay Population Model
In this paper, a nonlinear delay population model is investigated. Choosing the delay as a bifurcation parameter, we demonstrate that Hopf bifurcation will occur when the delay exceeds a critical value. Global existence of bifurcating periodic solutions is established. Numerical simulations supporting the theoretical findings are included.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1328678Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1403
 V. G. Nazarenko, Influence of delay on auto-oscillation in cell populations. Biofisika 21(1976)352-356.
 I. Kubiaczyk and S. H. Saker, Oscillation and stability in nonlinear delay differential equations of population dynamics. Math. Comput. Modelling 35(3-4)(2002)295-301.
 S. H. Saker and S. Agarwal, Oscillation and global attractivity in a nonlinear delay periodic model of population dynamics. Appl. Anal. 81(4)(2002)787-799.
 S. H. Saker, Periodic solutions, oscillation and attractivity of discrete nonlinear delay population model. Math. Comput. Modelling 47(3) (2008)278-297.
 Y. L. Song and Y. H. Peng, Periodic solution of a nonautonomous periodic model with continuous and discrete time. J. Comput. Anal. Math. 188(2)(2006)256-264.
 K. J. Zhang and Z. H. Wen, Periodic solution for a delayed population model on time scales. Int. J. Comput. Math. Sci. 4(3)(2010)166-168.
 Y. Kuang, Delay Differential Equations with Applications in Population Dynamics. Academic Press, INC, 1993.
 J. Hale,Theory of Functional Differential Equations. Springer-Verlag, 1977.
 Jianhong Wu, Symmetric functional differential equations and neural networks with memory. Transcations of AMS, 350(12)(1998)4799-4838.