Dynamical properties of max-plus equations obtained from tropically discretized Sel'kov model

2021/07/06 by Shousuke Ohmori, Ohmori, Shousuke, Yoshihiro Yamazaki +1
Computer Science · Engineering · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Mathematical Physics (math-ph) #Neural Networks and Reservoir Computing #Nonlinear Photonic Systems #Optical Network Technologies

paper · pdf · doi:10.48550/arxiv.2107.02435

openalex publication_date 2021/07/06 · openalex created_date 2021/07/19 · openalex updated_date 2026/07/28

Abstract

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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