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Existence of heteroclinic orbits in a novel three-order dynamical system

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Chinese Physics B 2013年第11期22卷 232-238页

作者：胡瑀闵乐泉甄平 Beijing University of Science and Technology

In this paper, we design a novel three-order autonomous system. Numerical simulations reveal the complex chaotic behaviors of the system. By applying the undetermined coefficient method, we find a heteroclinic orbit in the system. As a result, the Si＇lnikov criterion along with some other given conditions guarantees that the system has both Smale horseshoes and chaos of horseshoe type.

关键词： novel chaotic system heteroclinic orbit Si'lnikov criterion undetermined coefticient method

A Note on Homoclinic or heteroclinic orbits for the Generalized Hénon Map

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Acta Mathematicae Applicatae Sinica 2016年第2期32卷 283-288页

作者： Yong-guo SHI College of Mathematics and Information Science Xinyang Normal UniversityXinyang 464000China Key Laboratory of Numerical Simulation of Sichuan Province College of Mathematics and Information ScienceNeijiang Normal UniversityNeijiang 641112China

An important problem in a given dynamical system is to determine the existence of a homoclinic orbit. We improve the results of Qin and Xiao [Nonlinearity, 20 （2007）, 2305-2317], who present some sufficient conditions for the existence of a homoclinic/heteroclinic orbit for the generalized H@non map. Moreover, an algorithm is presented to locate these homoclinic orbits.

关键词： reversible planar map homoclinic orbit heteroclinic orbit generalized Henon map

Bifurcations of heteroclinic loops

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Science China Mathematics 1998年第8期41卷 837-848页

作者：朱德明夏志宏 Department of Mathematics East China Normal University Shanghai China Department of Mathematics Northwestern University Evanston USA

By generalizing the Floquet method from periodic systems to systems with exponential dichotomy, a local coordinate system is established in a neighborhood of the heteroclinic loop \%Γ\% to study the bifurcation problems of homoclinic and periodic orbits. Asymptotic expressions of the bifurcation surfaces and their relative positions are given. The results obtained in literature concerned with the 1\|hom bifurcation surfaces are improved and extended to the nontransversal case. Existence regions of the 1\|per orbits bifurcated from Γ are described, and the uniqueness and incoexistence of the 1\|hom and 1\|per orbit and the inexistence of the 2\|hom and 2\|per orbit are also obtained.

关键词： heteroclinic orbit homoclinlc bifurcation periodic orbit bifurcation

orbits heteroclinic to Invariant Manifolds

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Acta Mathematica Sinica,English Series 1996年第4期12卷 372-373,375-378页

作者： Zhu Deming Department of Mathematics East China Normal University Shanghai, 200062 China Department of Mathematics East China Normal University Shanghai China

Using the theory of invariant manifolds, we give local expressions of the stable and unstable manifolds for normally hyperbolic invariant tori, and study the existence of transverse orbits heteroclinic to hyperbolic i... 详细信息

关键词： Invariant manifold Exponential dichotomy heteroclinic orbit Transversality

DYNAMIC PULL-IN INSTABILITY OF DOUBLE-SIDED ACTUATED NANO-TORSIONAL SWITCHES

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Acta Mechanica Solida Sinica 2015年第1期28卷 91-101页

作者： Hamid M.Sedighi Kourosh H.Shirazi Department of Mechanical Engineering Shahid Chamran University

A nonlinear frequency-amplitude relation is developed to investigate the vibrational amplitude effect on the dynamic pull-in instability of double-sided-actuated nano-torsional switches. The governing equation of a nano-electro-mechanical system pre-deformed by an electric field contains the quintic nonlinear term. The influences of basic parameters on the pull-in instability and natural frequency are investigated using a powerful analytical approach called the homotopy perturbation method. It is demonstrated that two terms in series expansion are sufficient to produce an acceptable solution. The numerical results obtained have verified the soundness of the asymptotic procedure. The phase portraits of the double-sided nano-torsionalactuator exhibit periodic, homoclinic and heteroclinic orbits.

关键词： homotopy perturbation method frequency-amplitude relationship double-sidedactuated nano-switch dynamic pull-in instability homoclinic orbit heteroclinic orbit

Chaotification for a class of nonlinear systems

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Chinese Physics B 2009年第5期18卷 1769-1773页

作者：刘娜关治洪 Department of Control Science and Engineering Huazhong University of Science and Technology

More and more attention has been focused on effectively generating chaos via simple physical devices. The problem of creating chaotic attractors is considered for a class of nonlinear systems with backlash function in this paper. By utilizing the Silnikov heteroclinic and homoclinic theorems, some sufficient conditions are established to guarantee that the nonlinear system has horseshoe-type chaos. Examples and simulations are given to verify the effectiveness of the theoretical results.

关键词： chaos backlash function heteroclinic orbit chaos generation

ANOMALOUS DYNAMICS RESPONSE OF NONLINEAR ELASTIC BAR

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Applied Mathematics and Mechanics(English Edition) 2000年第9期21卷 1008-1015页

作者：张年梅韩强杨桂通徐秉业 Department of Engineering Mechanics Tsinghua University Beijing P R China Institute of Applied Mechanics Taiyuan University of Technology Taiyuan P R China

The dynamics behavior of tension bar with periodic tension velocity was presented. Melnikov method war used to study the dynamic system. The results show that material nonlinear may result in anomalous dynamics response. The subharmonic bifurcation and chaos may occur in the determined system when the tension velocity exceeds the critical value.

关键词： subharmonic bifurcation heteroclinic orbit chaos Melnikov function

Spectral　Characteristics　of　Atmospheric　Turbulence　Model

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Communications in Nonlinear Science and Numerical Simulation 1996年第4期1卷 25-28页

作者： Guojun XIN Shida LIU Shikou LIU & Fuming LIANG (Dept. of Geophysics, Peking University, Beijing, 100871, P.R.China) Dept. of Geophysics Peking University Beijing 100871 P.R.China

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ＳｐｅｃｔｒａｌＣｈａｒａｃｔｅｒｉｓｔｉｃｓｏｆＡｔｍｏｓｐｈｅｒｉｃＴｕｒｂｕｌｅｎｃｅＭｏｄｅｌ１１ＴｈｅｐａｐｅｒｗａｓｒｅｃｅｉｖｅｄｏｎＯｃｔ．２５，１９９６ＧｕｏｊｕｎＸＩＮＳｈｉｄａＬＩＵＳｈｉｋｏｕＬＩＵ＆ＦｕｍｉｎｇＬＩＡＮＧ（Ｄ...

关键词： KdV-Burgers equation heteroclinic orbit turbulent spectrum

The Global Dynamics of a Class of Vector Fields in R3

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Acta Mathematica Sinica,English Series 2011年第12期27卷 2469-2480页

作者： Xin An ZHANG Zhao Jun LIANG Lan Sun CHEN School of Mathematics and Statistics Central China Normal University Wuhan 430079 P. R. China Institute of Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 P. R. China

In this paper, .we find a bridge connecting a class of vector fields in R3 with the planar vector fields and give a criterion of the existence of closed orbits, heteroclinic orbits *** orbits of a class of vector fields in R3. All the possible nonwandering sets of this class of vector fields fall into three classes：（i） singularities; （ii） closed orbits; （iii） graphs of unions of singularities and the trajectories connecting them. The necessary and sufficient conditions for the boundedness of the vector fields are also obtained.

关键词： Tangent vector field invariant cone heteroclinic orbit vector field