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Novel four-dimensional autonomous chaotic system generating one-,two-,three- and four-wing attractors

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Chinese Physics B 2011年第11期20卷 151-158页

作者：余飞王春华尹晋文徐浩 College of Information Science and Engineering Hunan University

In this paper, we propose a novel four-dimensional autonomous chaotic system. Of particular interest is that this novel system can generate one-, two, three- and four-wing chaotic attractors with the variation of a single parameter, and the multi-wing type of the chaotic attractors can be displayed in all directions. The system is simple with a large positive Lyapunov exponent and can exhibit some interesting and complicated dynamical behaviours. Basic dynamical properties of the four-dimensional chaotic system, such as equilibrium points, the poincare map, the bifurcation diagram and the Lyapunov exponents are investigated by using either theoretical analysis or numerical method. Finally, a circuit is designed for the implementation of the multi-wing chaotic attractors. The electronic workbench observations axe in good agreement with the numerical simulation results.

关键词： multi-wing chaotic attractors four-dimensional chaotic system poincare map bifurcation diagram

Impact of lubricant traction coefficient on cage's dynamic characteristics in high-speed angular contact ball bearing

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Chinese Journal of Aeronautics 2017年第2期30卷 827-835页

作者： Zhang Wenhu Deng Sier Chen Guoding Cui Yongcun School of Mechatronics Engineering Northwestern Polytechnical University Xi'an 710071 China School of Mechatronics Engineering Henan University of Science and Technology Luoyang 471003 China Collaborative Innovation Center of Major Machine Manufacturing in Liaoning Dalian 116024 China

In this paper,the formulas of elasto-hydrodynamic traction coefficients of three Chinese aviation lubricating oils,4109,4106 and 4050,were obtained by a great number of elastohydrodynamic traction *** nonlinear dynamics differential equations of high-speed angular contact ball bearing were built on the basis of dynamic theory of rolling bearings and solved by Gear Stiff（GSTIFF） integer algorithm with variable *** impact of lubricant traction coefficient on cage＇s dynamic characteristics in high-speed angular contact ball bearing was investigated,and poincare map was used to analyze the impact of three types of aviation lubricating oils on the dynamic response of cage＇s mass *** then,the period of dynamic response of cage＇s mass center and the slip ratio of cage were used to assess the stability of cage under various working *** results of this paper provide the theoretical basis for the selection and application of aviation lubricating oil.

关键词： Dynamic characteristic High-speed angular contact ball bearing Lubricant traction coefficient poincare map Stability

Topological horseshoe in nonlinear Bloch system

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Chinese Physics B 2010年第12期19卷 105-108页

作者：樊庆菊 Department of Control Science and Engineering Huazhong University of Science and Technology Department of Statistics School of ScienceWuhan University of Technology

This paper demonstrates rigorous chaotic dynamics in nonlinear Bloch system by virtue of topological horseshoe and numerical method. It considers a properly chosen cross section and the corresponding poincare map, and shows the existence of horseshoe in the poincare map. In this way, a rigorous verification of chaos in the nonlinear Bloch system is presented.

关键词： Bloch equation chaos topological horseshoe poincare map

Lyapunov exponent calculation of a two-degree-of-freedom vibro-impact system with symmetrical rigid stops

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Chinese Physics B 2011年第4期20卷 123-131页

作者：李群宏谭洁燕 College of Mathematics and Information Science Guangxi University

A two-degree-of-freedom vibro-impact system having symmetrical rigid stops and subjected to periodic excitation is investigated in this paper. By introducing local maps between different stages of motion in the whole impact process, the poincare map of the system is constructed. Using the poincare map and the Gram Schmidt orthonormalization, a method of calculating the spectrum of Lyapunov exponents of the above vibro-impact system is presented. Then the phase portraits of periodic and chaotic attractors for the system and the corresponding convergence diagrams of the spectrum of Lyapunov exponents are given out through the numerical simulations. To further identify the validity of the aforementioned computation method, the bifurcation diagram of the system with respect to the bifurcation parameter and the corresponding largest Lyapunov exponents are shown.

关键词： vibro-impact system poincare map Gram-Schmidt orthonormalization Lyapunov exponent

Optimal and Memristor-Based Control of A Nonlinear Fractional Tumor-Immune Model

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Computers, Materials & Continua 2021年第6期67卷 3463-3486页

作者： Amr M.S.Mahdy Mahmoud Higazy Mohamed S.Mohamed Department of Mathematics College of ScienceTaif UniversityTaif21944Saudi Arabia Department of Mathematics Faculty of ScienceZagazig UniversityZagazig44519Egypt Department of Physics and Engineering Mathematics Faculty of Electronic engineeringMenoufia UniversityMenouf32952Egypt Department of Mathematics Faculty of ScienceAl-Azher UniversityNasr City11884Egypt

In this article,the reduced differential transform method is introduced to solve the nonlinear fractional model of *** fractional derivatives are described in the Caputo *** solutions derived using this method are easy and very *** model is given by its signal flow ***,a simulation of the system by the Simulink of MATLAB is *** disease-free equilibrium and stability of the equilibrium point are *** of a fractional optimal control for the cancer model is *** addition,to control the system,we propose a novel modification of its *** modification is based on converting the model to a memristive one,which is a first time in the literature that such idea is used to control this type of ***,we study the system’s stability via the Lyapunov exponents and poincare maps before and after *** order differential equations(FDEs)are commonly utilized to model systems that have memory,and exist in several physical phenomena,models in thermoelasticity field,and biological *** have been utilized to model the realistic biphasic decline manner of elastic systems and infection of diseases with a slower rate of *** are more useful than integer-order in modeling sophisticated models that contain physical phenomena.

关键词： RDTM tumor-immune optimal control caputo derivative signal flow simulink disease-free equilibrium stability memristive lyapunov exponents poincare map

Homoclinic and Periodic Orbits Arising Near the Heteroclinic Cycle Connecting Saddle-focus and Saddle Under Reversible Condition

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Acta Mathematica Sinica,English Series 2007年第8期23卷 1495-1504页

作者： De Ming ZHU Ying SUN Department of Mathematics East China Normal University Shanghai 200062 P. R. China School of Science University of Ji'nan Ji'nan 250022 P. R. China

In this paper, we study the dynamical behavior for a 4-dimensional reversible system near its heteroclinic loop connecting a saddle-focus and a saddle. The existence of infinitely many reversible 1-homoclinic orbits to the saddle and 2-homoclinic orbits to the saddle-focus is shown. And it is also proved that, corresponding to each 1-homoclinic （resp. 2-homoclinic） orbit F, there is a spiral segment such that the associated orbits starting from the segment are all reversible 1-periodic （resp. 2-periodic） and accumulate onto F. Moreover, each 2-homoclinic orbit may be also accumulated by a sequence of reversible 4-homoclinic orbits.

关键词： reversible condition homoclinic orbit poincare map periodic orbit saddle-focus

Reduced differential transform and Sumudu transform methods for solving fractional financial models of awareness

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Applied Mathematics(A Journal of Chinese Universities) 2023年第3期38卷 338-356页

作者： A.M.S.Mahdy K.A.Gepreel Kh.Lotfy A.El-Bary Department of Mathematics and Statistics College of ScienceTaif UniversityP.O.Box 11099Taif21944Saudi Arabia Department of Mathematics Faculty of ScienceZagazig UniversityP.O.Box 44519ZagazigEgypt Arab Academy for Science Technology and Maritime Transport1029AlexandriaEgypt

In that paper,we new study has been carried out on previous studies of one of the most important mathematical models that describe the global economic movement,and that is described as a non-linear fractional financial model of awareness,where the studies are represented at the steps following:One:The schematic of the model is ***:The disease-free equilibrium point(DFE)and the stability of the equilibrium point are ***:The stability of the model is fulfilled by drawing the Lyapunov exponents and poincare ***:The existence of uniformly stable solutions have ***:The Caputo is described as the fractional ***:Fractional optimal control for NFFMA is discussed by clarifying the fractional optimal control through drawing before and after ***:Reduced differential transform method(RDTM)and Sumudu Decomposition Method(SDM)are used to take the resolution of an ***,we display that SDM and RDTM are highly identical.

关键词： financial of awareness stability Lyapunov exponents poincare map fractional optimal control Hamiltonian

Bifurcations of Fine 3-point-loop in Higher Dimensional Space

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Acta Mathematica Sinica,English Series 2005年第1期21卷 39-52页

作者： YinLaiJIN DeMingZHU DepartmentofMathematics EastChinaNormalUniversityShanghai200062P.R.China DepartmentofMathematics LinyiTeachers'UniversityLinyi276005P.R.China//DepartmentofMathematicsEastChinaNormalUniversityShanghai200062P.R.China

By using the linear independent fundamental solutions of the linearvariational equation along the heteroclinic loop to establish a suitable local coordinate system insome small tubular neighborhood of the heteroclinic loop, the Poincaré map is constructed to studythe bifurcation problems of a fine 3–point loop in higher dimensional space. Under some transversalconditions and the non–twisted condition, the existence, coexistence and incoexistence of2–point–loop, 1–homoclinic orbit, simple 1–periodic orbit and 2–fold 1–periodic orbit, and thenumber of 1–periodic orbits are studied. Moreover, the bifurcation surfaces and existence regionsare given. Lastly, the above bifurcation results are applied to a planar system and an insidestability criterion is obtained.

关键词： Local coordinates poincare map 1–homoclinic orbit 1–periodic orbit Bifurcation surface

BIFURCATIONS OF ROUGH 3-POINT-LOOP WITH HIGHER DIMENSIONS

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Chinese Annals of Mathematics,Series B 2003年第1期24卷 85-96页

作者： JIN YINLAI ZHU DEMING ZHENG QINGYU Department of Mathematics Linyi Teachers' University Linyi 276005 Shandong China. Department of Mathematics East China Normal University Shanghai 200062 China.Department of Mathematics East China Normal University Shanghai 200062 China.Department of Mathematics Linyi Teachers' University Linyi 276005 Shandong China.

The authors study the bifurcation problems of rough heteroclinic loop connecting threesaddle points for the case β1 ＞ 1, β2 ＞ 1, β3 ＜ 1 and β1β2β3 ＜ 1. The existence, number, co-existence and incoexistence of 2-point-loop, 1-homoclinic orbit and 1-periodic orbit are ***, the bifurcation surfaces and existence regions are given.

关键词： Local coordinates poincare map 1-homoclinic orbit 1-periodic orbit Bifurcation surface