Reducing nonlinear dynamical systems to canonical forms.

Clicks: 298
ID: 72159
2018
Article Quality & Performance Metrics
Overall Quality
Not rated
Combines reader engagement with the AI quality analysis. This article has not been analysed, so there is no overall score — reader engagement is measured and shown alongside.
AI Quality Assessment
Not analyzed
Readership in this journal
Steady

Ranked #17 of 69 articles by views in philosophical transactions series a, mathematical, physical, and engineering sciences

Most read Least read

Bar heights use a square-root scale.

Mint this article as an NFT
Not yet minted

Create a permanent, verifiable on-chain record of this article on the Scimatic Network. The NFT is held in your Journament account, and you can withdraw it to your own wallet at any time.

5 SUSD one-off · no wallet required
Sign in to mint
Abstract
A global framework for treating nonlinear differential dynamical systems is presented. It rests on the fact that most systems can be transformed into the quasi-polynomial format. Any system in this format belongs to an infinite equivalence class characterized by two canonical forms, the Lotka-Volterra (LV) and the monomial systems. Both forms allow for finding total or partial integrability conditions, invariants and dimension reductions of the original systems. The LV form also provides Lyapunov functions and systematic tools for stability analysis. An abstract Lie algebra is shown to underlie the whole formalism. This abstract algebra can be expressed in several realizations among which are the bosonic creation-destruction operators. One of these representations allows one to obtain the analytic form of the general coefficient of the Taylor series representing the solution of the original system. This generates a new class of special functions that are solutions of these nonlinear dynamical systems. From the monomial canonical form, one can prove an equivalence relationship between urn processes and dynamical systems. This establishes a new link between nonlinear dynamics and stochastic processes.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 1)'.
Reference Key
brenig2018reducingphilosophical Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Brenig, Léon;
Journal philosophical transactions series a, mathematical, physical, and engineering sciences
Year 2018
DOI
20170384
URL
Keywords
nonlinear dynamics taylor series lie algebra lotka–volterra canonical form urn process

Citations

No citations found. To add a citation, contact the admin at info@scimatic.org

Comments

No comments yet. Be the first to comment on this article.