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学者姓名：李静
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Abstract ：
In this paper, we introduce a curvilinear coordinate transformation to study the bifurcation of periodic solutions from a 2-degree-of-freedom Hamiltonian system, when it is perturbed in Rm+4 , where m represents any positive integer. The extended Melnikov function is obtained by constructing a Poincar & eacute; map on the curvilinear coordinate frame of the trajectory of the unperturbed system. Then the criteria for bifurcation of periodic solutions of these Hamiltonian systems under isochronous and non-isochronous conditions are obtained. As for its application, we study the number of periodic solutions of a composite piezoelectric cantilever rectangular plate system whose averaged equation can be transformed into a (2+4)-dimensional dynamical system. Furthermore, under the two resonance conditions of 1:1 and 1:2, we obtain the periodic solution numbers of this system with the variation of para-metric excitation coefficient p(1).
Keyword ：
Periodic solutions Periodic solutions ( m+4 ) -dimension ( m+4 ) -dimension Bifurcation Bifurcation Curvilinear coordinate Curvilinear coordinate Extended Melnikov function Extended Melnikov function
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| GB/T 7714 | Quan, Tingting , Li, Jing , Sun, Min et al. Bifurcation of Multiple Periodic Solutions for a Class of Nonlinear Dynamical Systems in (m+4)-Dimension [J]. | JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS , 2024 , 31 (1) . |
| MLA | Quan, Tingting et al. "Bifurcation of Multiple Periodic Solutions for a Class of Nonlinear Dynamical Systems in (m+4)-Dimension" . | JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS 31 . 1 (2024) . |
| APA | Quan, Tingting , Li, Jing , Sun, Min , Chen, Yongqiang . Bifurcation of Multiple Periodic Solutions for a Class of Nonlinear Dynamical Systems in (m+4)-Dimension . | JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS , 2024 , 31 (1) . |
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Abstract ：
Purpose-This study aims to perform an in-depth analysis of double-diffusive natural convection (DDNC) in an irregularly shaped porous cavity. We investigate the convective heat transfer process induced by the lower wall treated as a heat source while the side walls of the enclosure are maintained at a lower temperature and concentration, and the remaining wall is adiabatic. Various factors, such as the Rayleigh number, Darcy effects, Hartmann number, Lewis number and effects of magnetic inclination are evaluated for their influence on flow dynamics and heat distribution. Design/methodology/approach-After validating the results, the FEM (finite element method) is used to simulate the flow pattern, temperature variations, and concentration by solving the nonlinear partial differential equations with the modified Rayleigh number (104 <= Ra <= 107), Darcy number (10-4 <= Da <= 10-1), Lewis number (0.1 <= Le <= 10), and Hartmann number 0 <= Ha <= 40 as the dimensionless operating parameters. Findings-The finding shows that the patterns of convection and the shape of the isotherms within porous enclosures are notably affected by the angle of the applied magnetic field. This study enhances our understanding of how double-diffusive natural convection (DDNC) operates in these enclosures, which helps improve heating and cooling technologies in various engineering fields. Research limitations/implications-Numerical and experimental extensions of the present study make it possible to investigate differences in thermal performance as a result of various curvatures, orientations, boundary conditions, and the use of three-dimensional analysis and other working fluids. Practical implications-The geometry configurations used in this study have wide-ranging applications in engineering fields, such as in heat exchangers, crystallization, microelectronics, energy storage, mixing, food processing, and biomedical systems. Originality/value-This study shows how an inclined magnetic field affects double-diffusive natural convection (DDNC) within a porous system featuring an irregularly shaped cavity, considering various multiphysical conditions.
Keyword ：
irregular cavity irregular cavity FEM FEM 65-XX 65-XX double diffusive double diffusive MHD MHD
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| GB/T 7714 | Chuhan, Imran Shabir , Li, Jing , Ahmed, Muhammad Shafiq et al. Numerical Investigation of Double-Diffusive Convection in an Irregular Porous Cavity Subjected to Inclined Magnetic Field Using Finite Element Method [J]. | MATHEMATICS , 2024 , 12 (6) . |
| MLA | Chuhan, Imran Shabir et al. "Numerical Investigation of Double-Diffusive Convection in an Irregular Porous Cavity Subjected to Inclined Magnetic Field Using Finite Element Method" . | MATHEMATICS 12 . 6 (2024) . |
| APA | Chuhan, Imran Shabir , Li, Jing , Ahmed, Muhammad Shafiq , Samuilik, Inna , Aslam, Muhammad Aqib , Manan, Malik Abdul . Numerical Investigation of Double-Diffusive Convection in an Irregular Porous Cavity Subjected to Inclined Magnetic Field Using Finite Element Method . | MATHEMATICS , 2024 , 12 (6) . |
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Abstract ：
为了拓展非线性量子差分方程共振边值问题的基本理论，研究了一类无穷区间上非线性量子差分方程共振边值问题。首先，通过构造合适的Banach空间，定义Fredholm算子，计算其核域和值域；其次，定义其他恰当的算子，并运用Mawhin重合度理论，建立该问题解的存在性定理；再次，运用反证法获得该问题解的唯一性结果；最后，给出一个例子说明主要结果的有效性。结果表明，在非线性项满足一定增长的条件下，非线性量子差分方程共振边值问题至少存在一个解。研究结果丰富了量子差分方程的可解性理论，为量子差分方程在数学、物理等领域的应用提供了理论参考。
Keyword ：
共振 共振 量子差分方程 量子差分方程 非线性泛函分析 非线性泛函分析 无穷区间 无穷区间 Mawhin重合度理论 Mawhin重合度理论
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| GB/T 7714 | 禹长龙 , 李双星 , 李静 et al. 无穷区间上非线性q-差分方程共振问题的可解性 [J]. | 河北科技大学学报 , 2024 , 45 (02) : 168-175 . |
| MLA | 禹长龙 et al. "无穷区间上非线性q-差分方程共振问题的可解性" . | 河北科技大学学报 45 . 02 (2024) : 168-175 . |
| APA | 禹长龙 , 李双星 , 李静 , 王菊芳 . 无穷区间上非线性q-差分方程共振问题的可解性 . | 河北科技大学学报 , 2024 , 45 (02) , 168-175 . |
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Abstract ：
Chaotic response is a robust effect in natural systems, and it is usually unfavorable for applications owing to uncertainty. In this paper, we propose several control strategies to stabilize the chaotic rhythm of a fractional piecewise-smooth oscillator. First, the Melnikov analysis is applied to the system, and the critical condition for the occurrence of homoclinic chaos is scrupulously established. Then, by applying appropriate control mechanisms, including delayed feedback control and periodic excitations, to the system, we can eliminate the zeros in the original Melnikov function, which serve as sufficient criteria for chaos suppression. Numerical simulations further demonstrate the accuracy of the theoretical results and the validity of the control schemes. Finally, the effects of parameter variations on the efficiency of control strategies are investigated. Note that we use the complex Simpson formula to calculate the complicated Melnikov functions presented in this paper. The current work may open a new innovative path to detect and control the chaotic dynamics of fractional non-smooth models.
Keyword ：
Fractional piecewise-smooth system Fractional piecewise-smooth system Chaos suppression Chaos suppression Melnikov analysis Melnikov analysis Homoclinic chaos Homoclinic chaos Complex simpson formula Complex simpson formula
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| GB/T 7714 | Zhang, Yufeng , Li, Jing , Zhu, Shaotao et al. Chaos detection and control of a fractional piecewise-smooth system with nonlinear damping [J]. | CHINESE JOURNAL OF PHYSICS , 2024 , 90 : 885-900 . |
| MLA | Zhang, Yufeng et al. "Chaos detection and control of a fractional piecewise-smooth system with nonlinear damping" . | CHINESE JOURNAL OF PHYSICS 90 (2024) : 885-900 . |
| APA | Zhang, Yufeng , Li, Jing , Zhu, Shaotao , Zhao, Hongzhen . Chaos detection and control of a fractional piecewise-smooth system with nonlinear damping . | CHINESE JOURNAL OF PHYSICS , 2024 , 90 , 885-900 . |
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Abstract ：
Dynamic vibration absorbers (DVAs) are widely used in engineering practice because of their good vibration control performance. Structural design or parameter optimization could improve its control efficiency. In this paper, the viscoelastic Maxwell-type DVA model with an inerter and multiple stiffness springs is investigated with the combination of the traditional theory and an intelligent algorithm. Firstly, the expressions and approximate optimal values of the system parameters are obtained using the fixed-point theory to deal with the H infinity optimization problem, which can provide help with the range of parameters in the algorithm. Secondly, we innovatively introduce the particle swarm optimization (PSO) algorithm to prove that the algorithm could adjust the value of the approximate solution to minimize the maximum amplitude by analyzing and optimizing the single variable and four variables. Furthermore, the validity of the parameters is further verified by simulation between the numerical solution and the analytical solution using the fourth-order Runge-Kutta method. Finally, the DVA demonstrated in this paper is compared with typical DVAs under random excitation. The timing sequence and variances, as well as the decreased ratios of the displacements, show that the presented DVA has a more satisfactory control performance. The inerter and negative stiffness spring can indeed bring beneficial effects to the vibration absorber. Remarkably, the intelligent algorithm can make the resonance peaks equal in the parameter optimization of the vibration absorber, which is quite difficult to achieve with theoretical methods at present. The results may provide a theoretical and computational basis for the optimization design of DVA.
Keyword ：
dynamic vibration absorber dynamic vibration absorber inerter inerter Maxwell-type Maxwell-type particle swarm optimization algorithm particle swarm optimization algorithm negative stiffness negative stiffness
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| GB/T 7714 | Chen, Yuying , Li, Jing , Zhu, Shaotao et al. Further Optimization of Maxwell-Type Dynamic Vibration Absorber with Inerter and Negative Stiffness Spring Using Particle Swarm Algorithm [J]. | MATHEMATICS , 2023 , 11 (8) . |
| MLA | Chen, Yuying et al. "Further Optimization of Maxwell-Type Dynamic Vibration Absorber with Inerter and Negative Stiffness Spring Using Particle Swarm Algorithm" . | MATHEMATICS 11 . 8 (2023) . |
| APA | Chen, Yuying , Li, Jing , Zhu, Shaotao , Zhao, Hongzhen . Further Optimization of Maxwell-Type Dynamic Vibration Absorber with Inerter and Negative Stiffness Spring Using Particle Swarm Algorithm . | MATHEMATICS , 2023 , 11 (8) . |
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Abstract ：
The dynamic vibration absorber (DVA) is widely used in engineering models with complex vibration modes. The research on the stability and periodic motions of the DVA model plays an important role in revealing its complex vibration modes and energy transfer. The aim of this paper is to study the stability and periodic motions of a two-degrees-of-freedom system coupled with an encapsulated nonsmooth dynamic vibration absorber under low-frequency forced excitation. Based on the slow-fast method, the model is transformed into a six-dimensional piecewise smooth system coupling two time scales. The existence and stability of the admissible equilibrium points for the model are discussed under different parameter conditions. Based on the first integrals, the Melnikov vector function of the nonsmooth dynamic vibration absorber model is calculated. The existence and number of periodic orbits bifurcated from a family of periodic orbits under different parameters are discussed. The phase diagram configuration of periodic orbits is given based on numerical simulation. The results obtained in this paper offer a new perspective for vibration analysis and parameter control for nonsmooth dynamic vibration absorbers.
Keyword ：
nonsmooth dynamic vibration absorber nonsmooth dynamic vibration absorber periodic motions periodic motions Melnikov function Melnikov function stability stability
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| GB/T 7714 | Guo, Ziyu , Li, Jing , Zhu, Shaotao et al. Stability and Periodic Motions for a System Coupled with an Encapsulated Nonsmooth Dynamic Vibration Absorber [J]. | APPLIED SCIENCES-BASEL , 2023 , 13 (15) . |
| MLA | Guo, Ziyu et al. "Stability and Periodic Motions for a System Coupled with an Encapsulated Nonsmooth Dynamic Vibration Absorber" . | APPLIED SCIENCES-BASEL 13 . 15 (2023) . |
| APA | Guo, Ziyu , Li, Jing , Zhu, Shaotao , Zhang, Yufeng . Stability and Periodic Motions for a System Coupled with an Encapsulated Nonsmooth Dynamic Vibration Absorber . | APPLIED SCIENCES-BASEL , 2023 , 13 (15) . |
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Abstract ：
In this paper, we study the bifurcation of periodic orbits for high-dimensional piecewise smooth near integrable systems defined in three regions separated by two switching manifolds. We assume that the unperturbed system has a family of periodic orbits which cross two switching manifolds transversely. The expression of Melnikov function is derived based on the first integral. And the conditions of periodic orbits bifurcated from a family of periodic orbits for the high-dimensional piecewise smooth near integrable system are obtained. The theoretical results are applied to the bifurcation analysis of periodic orbits of two-degree-of-freedom piecewise smooth system of nonlinear energy sink. The periodic orbits configurations are presented with numerical method and the number of periodic orbits is three. (c) 2022 Elsevier B.V. All rights reserved.
Keyword ：
High -dimensional systems High -dimensional systems Melnikov method Melnikov method Bifurcation of periodic orbits Bifurcation of periodic orbits Piecewise smooth Piecewise smooth
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| GB/T 7714 | Li, Jing , Guo, Ziyu , Zhu, Shaotao et al. Bifurcation of periodic orbits and its application for high-dimensional piecewise smooth near integrable systems with two switching manifolds [J]. | COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION , 2023 , 116 . |
| MLA | Li, Jing et al. "Bifurcation of periodic orbits and its application for high-dimensional piecewise smooth near integrable systems with two switching manifolds" . | COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION 116 (2023) . |
| APA | Li, Jing , Guo, Ziyu , Zhu, Shaotao , Gao, Ting . Bifurcation of periodic orbits and its application for high-dimensional piecewise smooth near integrable systems with two switching manifolds . | COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION , 2023 , 116 . |
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Abstract ：
Based on the relevant theories of M-matrix and the Lyapunov stability technique, this paper investigates the multistability of equilibrium points and periodic solutions for Clifford-valued memristive Cohen-Grossberg neural networks. With the help of Cauchy convergence criterion, the exponential stability inequality is derived. The system has [Pi(A)(K-A+1)](n) locally exponentially stable equilibrium points and periodic solutions, which greatly increases the number of solutions compared with the existing Cohen-Grossberg neural networks, where the K-A is a Clifford-valued and there is no limitation of linearity and monotonicity for activation functions. Furthermore, the attraction basins of stable periodic solutions are obtained, and it is proved that the basins can be enlarged. It is worth mentioning that the results can also be used to discuss the multistability of equilibrium points, periodic solutions, and almost periodic solutions for real-valued, complex-valued, and quaternion-valued memristive Cohen-Grossberg neural networks. Finally, two numerical examples with simulations are taken to verify the theoretical analysis.
Keyword ：
multistability multistability Clifford-valued Clifford-valued equilibrium points equilibrium points memristive Cohen-Grossberg neural networks memristive Cohen-Grossberg neural networks periodic solutions periodic solutions
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| GB/T 7714 | Li, Jing , Zhao, Hongzhen , Zhang, Yan et al. Multistability of equilibrium points and periodic solutions for Clifford-valued memristive Cohen-Grossberg neural networks with mixed delays [J]. | MATHEMATICAL METHODS IN THE APPLIED SCIENCES , 2023 , 47 (4) : 2679-2701 . |
| MLA | Li, Jing et al. "Multistability of equilibrium points and periodic solutions for Clifford-valued memristive Cohen-Grossberg neural networks with mixed delays" . | MATHEMATICAL METHODS IN THE APPLIED SCIENCES 47 . 4 (2023) : 2679-2701 . |
| APA | Li, Jing , Zhao, Hongzhen , Zhang, Yan , Zhu, Shaotao , Zhang, Yuzhan . Multistability of equilibrium points and periodic solutions for Clifford-valued memristive Cohen-Grossberg neural networks with mixed delays . | MATHEMATICAL METHODS IN THE APPLIED SCIENCES , 2023 , 47 (4) , 2679-2701 . |
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Abstract ：
This study investigates the impact of an inclined magnetic field (MHD) on entropy generation in double diffusive natural convective flow in a wavy enclosure filled with a non-Newtonian Casson fluid. The Galerkin Finite Element Method (GFEM) is employed to numerically solve the standard formulation, utilizing quadratic polynomials for momentum interpolation and a linear interpolating function for model approximation. The discretized system is resolved using Newton's approach and PARDISO's matrix factorization. Through simulations of varying ranges of Rayleigh numbers (1e(3) <= Ra <= 1e(5)), Casson parameter (0.1 <= beta <= 10), Hartmann numbers (0 <= Ha <= 40), Lewis numbers (0.1 <= Le <= 5), and inclined angle gamma (0 <= gamma <= 60o), the study provides valuable insights into the behavior of double diffusive natural convection in the wavy enclosure. Isotherms, iso-concentration contours, and streamlines are analyzed to assess different input distributions, and the study presents graphical representations and tabular data on heat transfer, mass transfer rate, and entropy production.
Keyword ：
wavy cavity wavy cavity Casson fluid Casson fluid GFEM GFEM magnetic field (MHD) magnetic field (MHD) double diffusive double diffusive
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| GB/T 7714 | Chuhan, Imran Shabir , Li, Jing , Guo, Ziyu et al. Entropy optimization of MHD non-Newtonian fluid in a wavy enclosure with double diffusive natural convection [J]. | NUMERICAL HEAT TRANSFER PART A-APPLICATIONS , 2023 , 85 (16) : 2703-2723 . |
| MLA | Chuhan, Imran Shabir et al. "Entropy optimization of MHD non-Newtonian fluid in a wavy enclosure with double diffusive natural convection" . | NUMERICAL HEAT TRANSFER PART A-APPLICATIONS 85 . 16 (2023) : 2703-2723 . |
| APA | Chuhan, Imran Shabir , Li, Jing , Guo, Ziyu , Shahzad, Hasan , Yaqub, Muhammad . Entropy optimization of MHD non-Newtonian fluid in a wavy enclosure with double diffusive natural convection . | NUMERICAL HEAT TRANSFER PART A-APPLICATIONS , 2023 , 85 (16) , 2703-2723 . |
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Abstract ：
Dynamic vibration absorbers (DVAs) are extensively used in the prevention of building and bridge vibrations, as well as in vehicle suspension and other fields, due to their excellent damping performance. The reliable optimization of DVA parameters is key to improve their performance. In this paper, an H-8 optimization problem of a novel three-element-type DVA model including an inerter device and a grounded negative stiffness spring is studied by combining a traditional theory and an intelligent algorithm. Firstly, to ensure the system's stability, the specific analytical expressions of the optimal tuning frequency ratio, stiffness ratio, and approximate damping ratio with regard to the mass ratio and inerter-mass ratio are determined through fixed-point theory, which provides an iterative range for algorithm optimization. Secondly, the particle swarm optimization (PSO) algorithm is used to further optimize the four parameters of DVA simultaneously. The effects of the traditional fixed-point theory and the intelligent PSO algorithm are comprehensively compared and analyzed. The results verify that the effect of the coupling of the traditional theory and the intelligent algorithm is better than that of fixed-point theory alone and can make the two resonance peaks on the amplitude-frequency response curves almost equal, which is difficult to achieve using fixed-point theory alone. Finally, we compare the proposed model with other DVA models under harmonic and random excitation. By comparing the amplitude-frequency curves, stroke lengths, mean square responses, time history diagrams, variances and decrease ratios, it is clear that the established DVA has a good vibration absorption effect. The research results provide theoretical and algorithm support for designing more effective DVA models of the same type in engineering applications.
Keyword ：
three-element-type DVA three-element-type DVA negative stiffness negative stiffness particle swarm optimization algorithm particle swarm optimization algorithm H-8 optimization H-8 optimization inerter-mass inerter-mass
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| GB/T 7714 | Gao, Ting , Li, Jing , Zhu, Shaotao et al. H-8 Optimization of Three-Element-Type Dynamic Vibration Absorber with Inerter and Negative Stiffness Based on the Particle Swarm Algorithm [J]. | ENTROPY , 2023 , 25 (7) . |
| MLA | Gao, Ting et al. "H-8 Optimization of Three-Element-Type Dynamic Vibration Absorber with Inerter and Negative Stiffness Based on the Particle Swarm Algorithm" . | ENTROPY 25 . 7 (2023) . |
| APA | Gao, Ting , Li, Jing , Zhu, Shaotao , Yang, Xiaodong , Zhao, Hongzhen . H-8 Optimization of Three-Element-Type Dynamic Vibration Absorber with Inerter and Negative Stiffness Based on the Particle Swarm Algorithm . | ENTROPY , 2023 , 25 (7) . |
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