Local Hopf Bifurcation and Global Existence of Periodic Solutions in a TCP System

XU Chang-jin; TANG Xian-hua; LIAO Mao-xin

doi:10.3879/j.issn.1000-0887.2010.06.012

Volume 31 Issue 6

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XU Chang-jin, TANG Xian-hua, LIAO Mao-xin. Local Hopf Bifurcation and Global Existence of Periodic Solutions in a TCP System[J]. Applied Mathematics and Mechanics, 2010, 31(6): 745-755. doi: 10.3879/j.issn.1000-0887.2010.06.012

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Local Hopf Bifurcation and Global Existence of Periodic Solutions in a TCP System

doi: 10.3879/j.issn.1000-0887.2010.06.012

1.
School of Mathematical Science and Computing Technology, Central South University, Changsha 410083, P. R. China;

Received Date: 1900-01-01
Rev Recd Date: 2010-04-09
Publish Date: 2010-06-15

Abstract

Abstract

The dynamics of a TCP system described by a firs-torder non linear delay differential equations was investigated. Byanalyzing the associated characteristic tran scendental equation, the result thata sequence of Hopf bifurcations occurat the positive equilibrium as the delay passesth rough a sequence of critical values was obtained. Explicit algorithms for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions were derived by using the normal form theory and center manifold theory. Global existence of periodic solutions was also established by using the method of Wu [Trans Amer Math Soc, 1998, 350(12):4799-38].
- TCP system,
- stability,
- local Hopf bifurcation,
- global Hopf bifurcation,
- periodic solution

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References(13)

References

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