Abstract
AbstractWe study the dynamical properties of a discrete population model with diffusion. We survey the transcritical, pitchfork, and flip bifurcations of nonhyperbolic fixed points by using the center manifold theorem. For the degenerate fixed point with eigenvalues ±1 of the model, we obtain the normal form of the mapping by using the coordinate transformation. Then we give an approximating system of the normal form via an approximation by a flow. We give the local behavior near a degenerate equilibrium of the vector field by the blowup technique. By the conjugacy between the reflection of time-one mapping of a vector field and the model we obtain the stability and qualitative structures near the degenerate fixed point of the model. Finally, we carry out a numerical simulation to illustrate the analytical results of the model.
Funder
Fundation of Graduate Innovation Center in NUAA
National Natural Science Foundation of China
Special Funds for the Cultivation of Guangdong College Students Scientific and Technological Innovation
The Innovation and Developing School Project of Guangdong Province
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
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