On dynamical connection between continuous and tropical discretized dynamical systems in one-dimensional (Mathematical structures of integrable systems, their developments and applications)

OHMORI, Shousuke YAMAZAKI, Yoshihiro 京都大学

2023.11

概要

We discuss the relationship of stability and the local bifurcations between one-dimensional differential equations and their tropically discretized ones. The discretized time interval is introduced as a bifurcation parameter in the tropical discretized equation, and emergence condition of an additional bifurcation, flip bifurcation, is revealed. By reviewing the continuous dynamical systems with saddle node and pitchfork bifurcations treated in our previous study (S. Ohmori and Y. Yamazaki, J. Math. Phys. 61 122702 (2020)), correspondence of their dynamics to their tropical discrete equations is discussed.

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参考文献

[1] M. Murata, J. Diﬀer. Equations Appl. 19 1008 (2013).

[2] R. E. Mickens, Nonstandard ﬁnite diﬀerence models of diﬀerential equations, (World Scientiﬁc, Singapore, 1994).

[3] M. E. Alexander and S. M. Moghadas, Electron. J. Diﬀer. Eqn. Conf. 12 9 (2005).

[4] S. Ohmori and Y. Yamazaki, J. Math. Phys. 61 122702 (2020).

[5] Y. Yamazaki and S. Ohmori, J. Phys. Soc. Jpn. 90 103001 (2021).

[6] S. Ohmori and Y. Yamazaki, in preparation (arXiv:2103.16777v1).

[7] S. Ohmori and Y. Yamazaki, JSIAM Letters 14 127 (2022).

[8] S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos (SpringerVerlag, New York. 1990).

[9] S. Ohmori and Y. Yamazaki, J. Math. Phys. 64 042704 (2023).

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On dynamical connection between continuous and tropical discretized dynamical systems in one-dimensional (Mathematical structures of integrable systems, their developments and applications)

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Generalized Hydrodynamic Limit for the Box–Ball System

Box and ball system with numbered boxes and balls (Mathematical structures of integrable systems, their developments and applications)

On Soliton Solutions of the Anti-Self-Dual Yang-Mills Equations from the Perspective of Integrable Systems

Kosambi–Cartan–Chern Stability in the Intermediate Nonequilibrium Region of the Brusselator Model

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On dynamical connection between continuous and tropical discretized dynamical systems in one-dimensional (Mathematical structures of integrable systems, their developments and applications)

概要

この論文で使われている画像

関連論文

表紙・目次

Generalized Hydrodynamic Limit for the Box–Ball System

Box and ball system with numbered boxes and balls (Mathematical structures of integrable systems, their developments and applications)

On Soliton Solutions of the Anti-Self-Dual Yang-Mills Equations from the Perspective of Integrable Systems

Kosambi–Cartan–Chern Stability in the Intermediate Nonequilibrium Region of the Brusselator Model

参考文献