Chaotic dynamics and fractal analysis of nonstandard Hamiltonian systems

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Chaotic dynamics and fractal analysis of nonstandard Hamiltonian systems

Popis výsledku v původním jazyce

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&lt;acute accent&gt; maps obtained through the Poincare&lt;acute accent&gt; surface-of-section method used to analyze weakly perturbed Hamiltonian systems. In this study, we study Poincare&lt;acute accent&gt; 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&lt;acute accent&gt; 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.

Název v anglickém jazyce

Chaotic dynamics and fractal analysis of nonstandard Hamiltonian systems

Popis výsledku anglicky

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&lt;acute accent&gt; maps obtained through the Poincare&lt;acute accent&gt; surface-of-section method used to analyze weakly perturbed Hamiltonian systems. In this study, we study Poincare&lt;acute accent&gt; 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&lt;acute accent&gt; 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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/EH22_008%2F0004649" target="_blank" >EH22_008/0004649: Kvantové inženýrství a nanotechnologie</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2025

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

CHAOS SOLITONS &amp; FRACTALS

ISSN

0960-0779

e-ISSN

1873-2887

Svazek periodika

200

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

44

Strana od-do

116974

Kód UT WoS článku

001548200400022

EID výsledku v databázi Scopus

2-s2.0-105012306070