Fractional gradient system and generalized Birkhoff system

New fractional gradient representation of generalized Birkhoff system is studied. New definition of fractional gradient system for generalized Birkhoff system is given. New condition for generalized Birkhoff system transforms into arbitrary fractional-order (integer or non-integer) gradient system i...

Full description

Saved in:
Bibliographic Details
Published inActa mechanica Vol. 235; no. 6; pp. 3607 - 3619
Main Authors Wang, Peng, Liu, Bai-qiang
Format Journal Article
LanguageEnglish
Published Vienna Springer Vienna 01.06.2024
Subjects
Classical and Continuum Physics
Control
Dynamical Systems
Engineering
Engineering Fluid Dynamics
Engineering Thermodynamics
Heat and Mass Transfer
Original Paper
Solid Mechanics
Theoretical and Applied Mechanics
Vibration
Online AccessGet full text

Cover

More Information
Summary:New fractional gradient representation of generalized Birkhoff system is studied. New definition of fractional gradient system for generalized Birkhoff system is given. New condition for generalized Birkhoff system transforms into arbitrary fractional-order (integer or non-integer) gradient system is deduced. The fractional dynamical modelling method by fractional gradient system is also discussed. We apply our results into several classical nonlinear models, such as van der Pol equation, Hénon–Heiles equation and four-order generalized Birkhoff’s equation.
ISSN:0001-5970
1619-6937
DOI:10.1007/s00707-024-03900-7