The existence of Silnikov's orbit in four-dimensional Duffing's systems

Wei Li; Peng Cheng Xu

doi:10.1007/210255-003-0141-z

The existence of Silnikov's orbit in four-dimensional Duffing's systems

Wei Li^*, Peng Cheng Xu

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

The existence of Silnikov's orbits in a four-dimensional dynamical system is discussed. The existence of Silnikov's orbit resulting in chaotic dynamics is established by the fiber structure of invariant manifold and high-dimensional Melnikov method. Numerical simulations are given to demonstrate the theoretical analysis.

Original language	English
Pages (from-to)	677-690
Number of pages	14
Journal	Acta Mathematicae Applicatae Sinica
Volume	19
Issue number	4
DOIs	https://doi.org/10.1007/210255-003-0141-z
Publication status	Published - 2003
Externally published	Yes

Keywords

Duffing's systems
Melnikov method
Silnikov's abit

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10.1007/210255-003-0141-z

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title = "The existence of Silnikov's orbit in four-dimensional Duffing's systems",

abstract = "The existence of Silnikov's orbits in a four-dimensional dynamical system is discussed. The existence of Silnikov's orbit resulting in chaotic dynamics is established by the fiber structure of invariant manifold and high-dimensional Melnikov method. Numerical simulations are given to demonstrate the theoretical analysis.",

keywords = "Duffing's systems, Melnikov method, Silnikov's abit",

author = "Wei Li and Xu, {Peng Cheng}",

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T1 - The existence of Silnikov's orbit in four-dimensional Duffing's systems

AU - Li, Wei

AU - Xu, Peng Cheng

PY - 2003

Y1 - 2003

N2 - The existence of Silnikov's orbits in a four-dimensional dynamical system is discussed. The existence of Silnikov's orbit resulting in chaotic dynamics is established by the fiber structure of invariant manifold and high-dimensional Melnikov method. Numerical simulations are given to demonstrate the theoretical analysis.

AB - The existence of Silnikov's orbits in a four-dimensional dynamical system is discussed. The existence of Silnikov's orbit resulting in chaotic dynamics is established by the fiber structure of invariant manifold and high-dimensional Melnikov method. Numerical simulations are given to demonstrate the theoretical analysis.

KW - Duffing's systems

KW - Melnikov method

KW - Silnikov's abit

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U2 - 10.1007/210255-003-0141-z

DO - 10.1007/210255-003-0141-z

M3 - Article

AN - SCOPUS:33745823041

SN - 0168-9673

VL - 19

SP - 677

EP - 690

JO - Acta Mathematicae Applicatae Sinica

JF - Acta Mathematicae Applicatae Sinica

IS - 4

ER -

The existence of Silnikov's orbit in four-dimensional Duffing's systems

Abstract

Keywords

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