TITLE:
Noether’s Conservation Laws and Stability in Nonlinear Conservative Interactions
AUTHORS:
Lisa Uechi, Hiroshi Uechi
KEYWORDS:
Noether’s Theorem, Conservative Nonlinear Model, Conservation Laws and Stability in Complex Systems
JOURNAL NAME:
Open Access Library Journal,
Vol.3 No.7,
July
29,
2016
ABSTRACT:
We reviewed a nonlinear dynamical model in 2n-variables which has conservative nonlinear interactions defined
in terms of Noether’s theorem in dynamics. The 2-variable (n = 1) conservative nonlinear model with external perturbations
produced a possible explanation for problems such as the 10-year cycles of
Canadian Lynx and snowshoe hair, interactions of microbes, stability and
conservation law of nonlinear interacting systems. In this paper, the atto-fox
(10-18-fox) problem on the LV nonlinear equation, properties of
4-variable conservative nonlinear interactions different from nonconservative
nonlinear interactions are examined and emphasized. Properties of the
4-variable (n = 2) conservative
interaction model and a method to construct numerical solutions are discussed
by employing the 2-variable solution. The periodic times of component variables
and the net periodic time defined by superposition of component variables are
discussed in order to study stability of the net 4-variable system. With
symmetries and conservation laws, nonlinear analyses would be useful to study
microscopic and macroscopic complex systems.