Generalized Lorenz Canonical Form Revisited

0542173 - ÚTIA 2022 RIV SG eng J - Journal Article
Čelikovský, Sergej - Chen, G.
Generalized Lorenz Canonical Form Revisited.
International Journal of Bifurcation and Chaos. Roč. 31, č. 5 (2021), č. článku 2150079. ISSN 0218-1274. E-ISSN 1793-6551
R&D Projects: GA ČR(CZ) GA19-05872S
Institutional support: RVO:67985556
Keywords : Generalized Lorenz system * generalized Lorenz canonical form * hyperbolic generalized Lorenz system * hyperbolic generalized Lorenz canonical form.
OECD category: Electrical and electronic engineering
Impact factor: 2.450, year: 2021
Method of publishing: Limited access
http://library.utia.cas.cz/separaty/2021/TR/celikovsky-0542173.pdf https://www.worldscientific.com/doi/abs/10.1142/S0218127421500796

This paper completes the description of the generalized Lorenz system (GLS) and hyperbolic generalized Lorenz system (HGLS) along with their canonical forms (GLCF, HGLCF), mostly presented earlier, by deriving explicit state transformation formulas to prove the equivalenc between GLS and GLCF, as well as between HGLS and HGLCF. Consequently, complete formulations of the generalized Lorenz canonical systems and forms, and their hyperbolic settings, are obtained and presented. Only potentially chaotic systems are classified, which significantly helps clarify the respective canonical forms. To do so, some tools for systems to exclude chaotic behavior are developed, which are interesting in their own right for general dynamical systems theory. The new insight may inspire future investigations of generalized and canonical formulations of some other types of chaotic systems.
Permanent Link: http://hdl.handle.net/11104/0320102