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
Citation: 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

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

doi: 10.3879/j.issn.1000-0887.2010.06.012
  • Received Date: 1900-01-01
  • Rev Recd Date: 2010-04-09
  • Publish Date: 2010-06-15
  • 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].
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