Chaotic dynamics and fractal analysis of nonstandard Hamiltonian systems
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F63839172%3A_____%2F25%3A10133793" target="_blank" >RIV/63839172:_____/25:10133793 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.chaos.2025.116974" target="_blank" >https://doi.org/10.1016/j.chaos.2025.116974</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.chaos.2025.116974" target="_blank" >10.1016/j.chaos.2025.116974</a>
Alternative languages
Result language
angličtina
Original language name
Chaotic dynamics and fractal analysis of nonstandard Hamiltonian systems
Original language description
Complex dynamical systems governed by nonstandard Lagrangians displaying non-natural forms of kinetic energy terms have recently received particular attention due to their relevance in the theory of differential equations and various fields of science and engineering. Such Lagrangians lead to nonstandard Hamiltonians that have relevance in various nonlinear complex dynamical systems governed by autonomous differential equations. Although guessing the forms of nonstandard Lagrangians requires solid mathematical methodologies, new types of these non-natural Lagrangians have been introduced recently in literature. It is also well-known that nonintegrable Hamiltonian systems with two or more degrees of freedom usually involve chaotic dynamics. Besides, stochasticity and resonance arise in 2-dimensional nonlinear Hamiltonian systems, and the chaos in the stochastic layer is generated by the main resonance interaction. The generation of chaotic trajectories in Hamiltonian systems has Poincare<acute accent> maps obtained through the Poincare<acute accent> surface-of-section method used to analyze weakly perturbed Hamiltonian systems. In this study, we study Poincare<acute accent> maps for two different types of nonstandard Hamiltonians generated from nonstandard Lagrangians, and we analyze some of their relevant chaotic properties based on the largest Lyapunov exponents and the bifurcation diagrams. Additionally, we compute the fractal dimension and Hurst exponent of these Poincare<acute accent> sections, revealing varying degrees of chaos. The results show that fractal dimension values range between 1.76 and 1.90, while Hurst exponent values remain below 0.5, concerning the presence of anti-persistent chaotic behavior. Several emergent features related to chaotic behavior and fractal structures are observed. Our approach provides a new perspective on assessing the robustness of nonlinear dynamical systems governed by nonstandard Hamiltonians.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
<a href="/en/project/EH22_008%2F0004649" target="_blank" >EH22_008/0004649: Quantum Engineering and Nanotechnology</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
CHAOS SOLITONS & FRACTALS
ISSN
0960-0779
e-ISSN
1873-2887
Volume of the periodical
200
Issue of the periodical within the volume
1
Country of publishing house
DE - GERMANY
Number of pages
44
Pages from-to
116974
UT code for WoS article
001548200400022
EID of the result in the Scopus database
2-s2.0-105012306070