The existence of $ \omega $-limit set for a modified Nosé-Hoover oscillator-Reference-Cited by-同舟云学术

The existence of $ \omega $-limit set for a modified Nosé-Hoover oscillator

Published:2022 Issue:12 Volume:27 Page:7275
ISSN:1531-3492
Container-title:Discrete and Continuous Dynamical Systems - B
language:
Short-container-title:DCDS-B

Author:

Han Qianqian¹,Deng Bo²,Yang Xiao-Song³⁴

Affiliation:

1. School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou, Henan 450046, China

2. Department of mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588, USA

3. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China

4. Hubei Key Laboratory of Engineering Modeling and Science Computing, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China

Abstract

<p style='text-indent:20px;'>In this paper, we prove the existence of <inline-formula><tex-math id="M2">\begin{document}$ \omega $\end{document}</tex-math></inline-formula>-limit set for a modified Nosé-Hoover oscillator. We also prove the existence of either an invariant torus or a stable periodic orbit of the oscillator. In addition, we show by numerical simulations the co-existence of both <inline-formula><tex-math id="M3">\begin{document}$ \alpha $\end{document}</tex-math></inline-formula>- and <inline-formula><tex-math id="M4">\begin{document}$ \omega $\end{document}</tex-math></inline-formula>-limit sets of various types of periodic orbits, invariant tori, and chaotic attractors.</p>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics

Reference11 articles.

1. C. Chicone, Ordinary Differential Equations with Applications, 2$^{nd}$ edition, Springer, New York, 2006.

2. W. G. Hoover.Canonical dynamics: Equilibrium phase-space distributions, Phys. Rev. A, 31 (1985), 1695-1697.

3. W. G. Hoover.Remark on "Some simple chaotic flows", Physical Review E, 51 (1995), 759-759.

4. W. G. Hoover.Nosé–Hoover nonequilibrium dynamics and statistical mechanics, Molecular Simulation, 33 (2007), 13-19.

5. S. Nosé.A unified formulation of the constant temperature molecular dynamics methods, Journal of Chemical Physics, 81 (1984), 511-519.

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