热带离散Sel'kov模型的Max-plus方程的动力学性质
Dynamical properties of max-plus equations obtained from tropically discretized Sel'kov model
摘要：
通过超离散化方法，从热带离散的Sel'kov模型导出了Max-plus方程。这些最大加方程具有与离散模型相同的动力学结构：Neimark-Sacker分岔和极限环。超离散极大值方程的极限环有七个离散状态。此外，这些最大加方程表现出兴奋性。根据数值结果讨论了热带离散模式与导出的最大加值方程之间的关系。结果发现，导出的最大加方程对应于热带离散模式的极限情况。
英文摘要：
Max-plus equations are derived from tropically discretized Sel'kov model via ultradiscretization. These max-plus equations possess common dynamical structures with the discretized model: Neimark-Sacker bifurcation and limit cycles. The limit cycles of the ultradiscrete max-plus equations have seven discrete states. Furthermore, these max-plus equations exhibit excitability. Relationship between the tropically discretized model and the derived max-plus equations is also discussed based on numerical results. It is found that the derived max-plus equations correspond to a limiting case of the tropically discretized model.
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