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Stability and Hopf bifurcation analysis for a Lotka-Volterra predator-prey model with two delays

100%

Xu C. , Liao M. , He X.

tom Vol. 21, no 1

97-107

In this paper, a two-species Lotka-Volterra predator-prey model with two delays is considered. By analyzing the associated characteristic transcendental equation, the linear stability of the positive equilibrium is investigated and Hopf bifurcation is demonstrated. Some explicit formulae for determining the stability and direction of Hopf bifurcation periodic solutions bifurcating from Hopf bifurcations are obtained by using normal form theory and center manifold theory. Some numerical simulations for supporting the theoretical results are also included.

Nonlinear analysis of the stability of hydrodynamic bearings

84%

Amamou A. , Chouchane M. , Naimi S.

Diagnostyka

2009

tom nr 4(52)

3-10

The linear analysis of the stability of a hydrodynamic bearing is used to determine the stability boundaries and to predict if the steady state is stable or not. A nonlinear or weakly nonlinear model is used to determine the behaviour of the system near the critical stability boundaries. By applying the Hopf bifurcation theory, the existence of stable or unstable limit cycles in the neighbourhood of the stability boundaries can be predicted depending on the characteristics of the bearing.A numerical integration of the nonlinear equations of motion is then carried out in order to verify the results obtained analytically.