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Dynamical behavior for a stochastic two-species competitive model

100%
Xu C., Liao M.
Open Mathematics
|
2017
|
tom 15
|
nr 1
1258-1266
EN
This paper deals with a stochastic two-species competitive model. Some very verifiable criteria on the global stability of the positive equilibrium of the deterministic system are established. An example with its computer simulations is given to illustrate our main theoretical findings.
2
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Stability and Hopf bifurcation analysis for a Lotka-Volterra predator-prey model with two delays

81%
Xu C., Liao M., He X.
International Journal of Applied Mathematics and Computer Science
|
2011
|
tom 21
|
nr 1
97-107
EN
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.
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