论文标题
当霍普夫遇到马鞍：糖酵解的扩散塞尔科夫模型中的分叉
When Hopf meets saddle: bifurcations in the diffusive Selkov model for glycolysis
论文作者
论文摘要
我们研究了Selkov模型中的线性不稳定性和分叉，以扩散糖酵解。我们表明，该模型具有零波动矢量，有限的频率HOPF分叉，以增长的振荡性但空间均匀的状态和鞍形节点分叉，可与增长的不均匀状态，具有有限波形的稳定模式。我们进一步证明，通过调整两个浓度的相对扩散率，可以使两种不稳定性在参数空间中的同一点发生，从而导致不寻常的condimension-two-two分叉。然后，我们表明，在此分叉的附近，初始条件决定了长期限制出现在空间均匀的振荡或空间周期性的稳定模式中。
We study the linear instabilities and bifurcations in the Selkov model for glycolysis with diffusion. We show that this model has a zero wave-vector, finite frequency Hopf bifurcation to a growing oscillatory but spatially homogeneous state and a saddle-node bifurcation to a growing inhomogeneous state with a steady pattern with a finite wavevector. We further demonstrate that by tuning the relative diffusivity of the two concentrations, it is possible to make both the instabilities to occur at the same point in the parameter space, leading to an unusual type of codimension-two bifurcation. We then show that in the vicinity of this bifurcation the initial conditions decide whether a spatially uniform oscillatory or a spatially periodic steady pattern emerges in the long time limit.
