Direction of Hopf bifurcation in a delayed Lotka-Volterra competition diffusion system. (English) Zbl 1162.92044
Summary: This paper is concerned with a delayed Lotka-Volterra two species competition diffusion system with a single discrete delay and subject to homogeneous Dirichlet boundary conditions. The main purpose is to investigate the direction of Hopf bifurcations resulting from the increase of the delay. By applying the implicit function theorem, it is shown that the system under consideration can undergo a supercritical Hopf bifurcation near the spatially inhomogeneous positive stationary solution when the delay crosses through a sequence of critical values.
MSC:
| 92D40 | Ecology |
| 35B32 | Bifurcations in context of PDEs |
| 34K60 | Qualitative investigation and simulation of models involving functional-differential equations |
| 35Q80 | Applications of PDE in areas other than physics (MSC2000) |
Keywords:
time delay; competition diffusion; Dirichlet boundary conditions; Hopf bifurcation; directionReferences:
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