Fractional Noether theorem and fractional Lagrange equation of multi-scale mechano-electrophysiological coupling model of neuron membrane

doi:10.1088/1674-1056/ac9cbe

中国物理B ›› 2023, Vol. 32 ›› Issue (7): 74501-074501.doi: 10.1088/1674-1056/ac9cbe

Fractional Noether theorem and fractional Lagrange equation of multi-scale mechano-electrophysiological coupling model of neuron membrane

Peng Wang(王鹏)^†

School of Civil Engineering and Architecture, University of Jinan, Jinan 250022, China

收稿日期:2022-08-14 修回日期:2022-09-29 接受日期:2022-10-21 出版日期:2023-06-15 发布日期:2023-07-05
通讯作者: Peng Wang E-mail:cea_wangp@ujn.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12272148 and 11772141).

Fractional Noether theorem and fractional Lagrange equation of multi-scale mechano-electrophysiological coupling model of neuron membrane

Peng Wang(王鹏)^†

School of Civil Engineering and Architecture, University of Jinan, Jinan 250022, China

Received:2022-08-14 Revised:2022-09-29 Accepted:2022-10-21 Online:2023-06-15 Published:2023-07-05
Contact: Peng Wang E-mail:cea_wangp@ujn.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12272148 and 11772141).

摘要/Abstract

摘要： Noether theorem is applied to a variable order fractional multiscale mechano-electrophysiological model of neuron membrane dynamics. The variable orders fractional Lagrange equation of a multiscale mechano-electrophysiological model of neuron membrane dynamics is given. The variable orders fractional Noether symmetry criterion and Noether conserved quantities are given. The forms of variable orders fractional Noether conserved quantities corresponding to Noether symmetry generators solutions of the model under different conditions are discussed in detail, and it is found that the expressions of variable orders fractional Noether conserved quantities are closely dependent on the external nonconservative forces and material parameters of the neuron.

关键词: Hamilton's principle, Noether theorem, fractional derivative, multiscale electromechanical coupling, neuron membrane

Abstract: Noether theorem is applied to a variable order fractional multiscale mechano-electrophysiological model of neuron membrane dynamics. The variable orders fractional Lagrange equation of a multiscale mechano-electrophysiological model of neuron membrane dynamics is given. The variable orders fractional Noether symmetry criterion and Noether conserved quantities are given. The forms of variable orders fractional Noether conserved quantities corresponding to Noether symmetry generators solutions of the model under different conditions are discussed in detail, and it is found that the expressions of variable orders fractional Noether conserved quantities are closely dependent on the external nonconservative forces and material parameters of the neuron.

Key words: Hamilton's principle, Noether theorem, fractional derivative, multiscale electromechanical coupling, neuron membrane

中图分类号: (Lagrangian and Hamiltonian mechanics)

45.20.Jj

11.30.-j (Symmetry and conservation laws) 45.10.Hj (Perturbation and fractional calculus methods) 46.70.Hg (Membranes, rods, and strings)

Peng Wang(王鹏). Fractional Noether theorem and fractional Lagrange equation of multi-scale mechano-electrophysiological coupling model of neuron membrane[J]. 中国物理B, 2023, 32(7): 74501-074501.

Peng Wang(王鹏). Fractional Noether theorem and fractional Lagrange equation of multi-scale mechano-electrophysiological coupling model of neuron membrane[J]. Chin. Phys. B, 2023, 32(7): 74501-074501.

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Fractional Noether theorem and fractional Lagrange equation of multi-scale mechano-electrophysiological coupling model of neuron membrane

Fractional Noether theorem and fractional Lagrange equation of multi-scale mechano-electrophysiological coupling model of neuron membrane

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