• Kyungpook Mathematical Journal
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• v.50 no.2
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• pp.255-266
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• 2010

We consider a delayed predator-prey system with Holling II functional response. Firstly, the paper considers the stability and local Hopf bifurcation for a delayed prey-predator model using the basic theorem on zeros of general transcendental function, which was established by Cook etc.. Secondly, special attention is paid to the global existence of periodic solutions bifurcating from Hopf bifurcations. By using a global Hopf bifurcation result due to Wu, we show that the local Hopf bifurcation implies the global Hopf bifurcation after the second critical value of delay. Finally, several numerical simulations supporting the theoretical analysis are given.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.36 no.3
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• pp.301-307
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• 2012

The characteristics of pressure loss in an asymmetric bifurcating tube were investigated numerically for steady inspiratory conditions. The loss coefficient K calculated for various asymmetry and flow-distribution ratios found in human lung airways showed a power-law dependence on the Reynolds number (Re) and length-to-diameter ratio (L/d), with different exponents for Re $\geq$ 100 and Re < 100. The fundamental characteristics of the asymmetric bifurcation are similar to the case of symmetric bifurcation. In addition, the effect of skewed inlet velocity profiles on the pressure loss was weak, and decreased with an increasing number of bifurcations.