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Frequency Domain Analysis for Hopf Bifurcation in a Delayed Competitive Web-site Model
Abstract:In this paper, applying frequency domain approach, a delayed competitive web-site system is investigated. By choosing the parameter α as a bifurcation parameter, it is found that Hopf bifurcation occurs as the bifurcation parameter α passes a critical values. That is, a family of periodic solutions bifurcate from the equilibrium when the bifurcation parameter exceeds a critical value. Some numerical simulations are included to justify the theoretical analysis results. Finally, main conclusions are given.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1124121Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 967
 L.A. Adamic, B.A. Huberman, The nature of markets in the world wide web. Quart. J. Electronic Commence 1 (2000) 5-12.
 S.M. Maurer, B.A. Huberman, Competitive dynamics of web sites. J. Econ. Dynam. Control 27 (2003) 2195-2206.
 M. Xiao,J.D. Cao, Stability and Hopf bifurcation in a delayed competitive web sites model. Phys. Lett. A 353 (2006) 138-150.
 J.L. Zhang, J.H. Dou, Y. Shi, Hopf bifurcation of a competitive web-site system with reflexive and competition delays. Pure Appl. Math. 27 (2011) 51-54.(in chinese)
 D.J. Allwright, Harmonic balance and the Hopf bifurcation theorem. Math. Proc. Cambridge Phil. Soc. 82 (1977) 453-467.
 A.I. Mees,L.O. Chua, The Hopf bifurcation theorem and its applications to nonlinear oscillations in circuits and systems. IEEE Trans. Circuits Syst. 26 (1979) 235-254.
 J.L. Moiola, G.R. Chen, Hopf bifurcation analysis: a frequency domain approach. Singapore: World Scientific, 1996.
 X.F. Liao, S.W. Li, Hopf bifurcation on a two-neuron system with distributed delays: a frequency domain approach. Nonlinear Dyn. 31 (2003) 299-326.
 X.F. Liao, S.W. Li,G.R. Chen, Bifurcation analysis on a two-neuron system with distributed delays in the frequency domain. Neural Netw. 17 ( 2004) 545-561.
 J.L. Moiola, G.R. Chen, Frequency domain approach to computational analysis of bifurcations and limit cycles: a tutorial. Int. J. Bifur. Chaos 3 (1993) 843-867.
 C.J. Xu, X.H. Tang,M.X. Liao, Frequency domain analysis for bifur cation in a simplified tri-neuron BAM network model with two delays. Neural Netw. 23 (2010) 872-880.