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学者姓名：李静
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Abstract ：
Nonlinear oscillators with multiple potential wells are widely used in practical structures such as vibration absorbers and energy harvesters due to their lower energy thresholds. The study of the chaotic characteristics of various homoclinic oscillators is of great significance for further understanding multi-stable systems, since homoclinic orbits characterize the boundary between different types of motion. The proper design of triple smooth-discontinuous (SD) oscillators can achieve four-well characteristics, and the elastic restoring force of the system can be approximated as a piecewise linear function. Unlike bistable and tri-stable oscillators, this oscillator exhibits multiple types of homoclinic orbits, and analytical expressions for these types of orbits are derived by analyzing the geometric structure of phase space. By utilizing the energy relationships of the Hamiltonian system and extending the Melnikov method, the threshold curves of these three types of homoclinic orbits are derived. Finally, the relationship between these threshold curves and the chaotic characteristics of the system is investigated through numerical simulations.
Keyword ：
Multiple homoclinic orbits Multiple homoclinic orbits Melnikov function Melnikov function Quadruple-well Quadruple-well Chaotic phenomena Chaotic phenomena
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| GB/T 7714 | Li, Jing , Sun, Ran , Zhu, Shaotao . Chaotic characteristics of a quadruple-well triple SD oscillator with multiple homoclinic orbits [J]. | NONLINEAR DYNAMICS , 2025 , 113 (11) : 13807-13835 . |
| MLA | Li, Jing 等. "Chaotic characteristics of a quadruple-well triple SD oscillator with multiple homoclinic orbits" . | NONLINEAR DYNAMICS 113 . 11 (2025) : 13807-13835 . |
| APA | Li, Jing , Sun, Ran , Zhu, Shaotao . Chaotic characteristics of a quadruple-well triple SD oscillator with multiple homoclinic orbits . | NONLINEAR DYNAMICS , 2025 , 113 (11) , 13807-13835 . |
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Abstract ：
The dry friction coupled vibration system represents a typical nonsmooth system, and the investigation of the dynamic characteristics of nonsmooth systems is of great significance for mechanical control, safe operation, and the formulation of engineering standards. In this paper, the theory of periodic orbits and bifurcations in a class of high-dimensional piecewise smooth discontinuous systems is explored in response to the need for mathematical theory and practical applications and is applied to study the dynamic characteristics of a two-degree-of-freedom dry friction coupled vibration system. A global Poincar & eacute; map is constructed, and the center manifold method for smooth systems is extended to derive sufficient and necessary conditions for the existence of an invariant cone. Based on Floquet theory, the stability of the invariant cone composed of periodic orbits is demonstrated. Additionally, the bifurcation phenomena and the persistence problem of the invariant cone are investigated. The parameter conditions for the periodic orbits generated by Hopf-like bifurcation induced by nonlinear disturbances are further considered, and the stability of periodic orbit is determined. The distribution configurations of the trajectories are obtained through numerical simulations to validate the accuracy of the theoretical findings. This work provides a solid theoretical foundation for parameter optimization and vibration control in high-dimensional dry friction coupled vibration systems within engineering practice.
Keyword ：
periodic orbit periodic orbit bifurcation bifurcation dry friction coupled vibration system dry friction coupled vibration system high-dimensional piecewise smooth discontinuous system high-dimensional piecewise smooth discontinuous system invariant cone invariant cone
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| GB/T 7714 | Cui, Yujiao , Li, Jing , Zhu, Shaotao et al. Periodic Orbits and Bifurcations in a High-Dimensional Nonautonomous Piecewise Smooth Discontinuous System [J]. | MATHEMATICAL METHODS IN THE APPLIED SCIENCES , 2025 . |
| MLA | Cui, Yujiao et al. "Periodic Orbits and Bifurcations in a High-Dimensional Nonautonomous Piecewise Smooth Discontinuous System" . | MATHEMATICAL METHODS IN THE APPLIED SCIENCES (2025) . |
| APA | Cui, Yujiao , Li, Jing , Zhu, Shaotao , Wang, Hongwu . Periodic Orbits and Bifurcations in a High-Dimensional Nonautonomous Piecewise Smooth Discontinuous System . | MATHEMATICAL METHODS IN THE APPLIED SCIENCES , 2025 . |
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Abstract ：
With the increasing performance requirements of vibration suppression devices for precision instruments and structural safety, there is an urgent need to explore efficient and stable vibration absorbers. This paper aims to investigate the response mechanism of a geometrically nonlinear coupled system under harmonic excitation, taking into account the damping of the primary system, which is often overlooked in research. The slow variation equation of the system is derived by the complexification-averaging method, from which the bifurcation analysis is conducted, and the influences of the two types of damping on the bifurcation are thoroughly discussed. Moreover, two motion triggering conditions are analyzed, namely, the threshold for the transition from intra-well periodic to inter-well chaos, and the threshold for the occurrence of strongly modulated response, some typical parameters are selected for numerical verification. Furthermore, the damping dissipation ratio is defined to evaluate the damping efficiency of the system, and the numerical results indicate that the optimal working efficiency can be achieved when the system first performs steady-state motion across two potential energy wells. Finally, the energy spectrum is calculated by the Romberg algorithm to verify the vibration reduction performance of the proposed model.
Keyword ：
response mechanism response mechanism bifurcation and chaos bifurcation and chaos geometrically nonlinear damping geometrically nonlinear damping Nonlinear energy sink Nonlinear energy sink
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| GB/T 7714 | Zhao, Hongzhen , Li, Jing , Zhu, Shaotao et al. Response Mechanism of Nonlinear Energy Sink with Geometrically Nonlinear Damping Attached to Damped Primary System [J]. | INTERNATIONAL JOURNAL OF STRUCTURAL STABILITY AND DYNAMICS , 2025 . |
| MLA | Zhao, Hongzhen et al. "Response Mechanism of Nonlinear Energy Sink with Geometrically Nonlinear Damping Attached to Damped Primary System" . | INTERNATIONAL JOURNAL OF STRUCTURAL STABILITY AND DYNAMICS (2025) . |
| APA | Zhao, Hongzhen , Li, Jing , Zhu, Shaotao , Zhang, Yufeng . Response Mechanism of Nonlinear Energy Sink with Geometrically Nonlinear Damping Attached to Damped Primary System . | INTERNATIONAL JOURNAL OF STRUCTURAL STABILITY AND DYNAMICS , 2025 . |
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Abstract ：
Low-frequency excitation is often challenging to fully absorb through internal energy dissipation systems, while grounding damping can effectively leverage the stability of the ground to absorb low-frequency energy, thereby mitigating the effects of low-frequency excitation on the primary structure. In this paper, the response mechanism of a grounded damping nonlinear energy sink (GNES) is investigated based on the complexification-averaging and multi-scale method. Furthermore, the impact of external excitation amplitude on the amplitude frequency curves is analyzed under two different primary system damping ratios, and the frequency threshold at which the GNES exhibits damping effect is identified. Besides, the vibration suppression region within the two-dimensional parameter space is partitioned into four distinct zones: the invalid region, saddle-node bifurcation region, effective damping region, and deterioration region. An in-depth analysis is conducted on the effects of varying system parameters on the damping region. Compared to the classical NES model, the numerical simulation results indicate that GNES achieves superior vibration reduction over a broader range of excitation frequencies. This finding holds substantial significance in enhancing the applicability of NES in broadband excitation environments.
Keyword ：
Complexification-averaging method Complexification-averaging method Strongly modulated response Strongly modulated response Grounded damping nonlinear energy sink Grounded damping nonlinear energy sink Effective damping Effective damping Bifurcation Bifurcation
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| GB/T 7714 | Zhao, Hongzhen , Li, Jing , Zhu, Shaotao et al. Research on damping region on grounded damping nonlinear energy sink [J]. | NONLINEAR DYNAMICS , 2025 . |
| MLA | Zhao, Hongzhen et al. "Research on damping region on grounded damping nonlinear energy sink" . | NONLINEAR DYNAMICS (2025) . |
| APA | Zhao, Hongzhen , Li, Jing , Zhu, Shaotao , Zhang, Yufeng . Research on damping region on grounded damping nonlinear energy sink . | NONLINEAR DYNAMICS , 2025 . |
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Abstract ：
The main aim of this paper is to investigate the oscillatory behavior of solutions for nonlinear Riemann-Liouville fractional (p, q)-difference equations. We obtain sufficient conditions for the oscillation of solutions using Young's inequality and various other inequalities. Additionally, we present results by substituting the Riemann-Liouville (p, q)-differential operator with the Caputo (p, q)-fractional difference operator. It is noteworthy that some MATLAB codes for the (p, q)-analogues, (p, q)-derivatives, (p, q)-integrals, and (p, q)-gamma functions are provided. Finally, two illustrative examples validate the main theorems presented in this paper.
Keyword ：
MATLAB MATLAB oscillation theory oscillation theory fractional (p, q)-difference equations fractional (p, q)-difference equations Young's inequality Young's inequality
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| GB/T 7714 | Yu, Changlong , Li, Shuangxing , Li, Jing et al. Oscillation criteria for nonlinear fractional (p, q)-difference equations [J]. | PHYSICA SCRIPTA , 2025 , 100 (1) . |
| MLA | Yu, Changlong et al. "Oscillation criteria for nonlinear fractional (p, q)-difference equations" . | PHYSICA SCRIPTA 100 . 1 (2025) . |
| APA | Yu, Changlong , Li, Shuangxing , Li, Jing , Wang, Jufang . Oscillation criteria for nonlinear fractional (p, q)-difference equations . | PHYSICA SCRIPTA , 2025 , 100 (1) . |
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Abstract ：
This paper investigates the bifurcation, chaos, and active control of a mixed Rayleigh-Li & eacute;nard oscillator with mixed time delays. First, the effects of system parameters on the supercritical pitchfork bifurcations are discussed in detail by applying the fast-slow separation method. Second, it is rigorously proved by the Melnikov method that chaotic vibration exists when the parameters of the uncontrolled system are selected above the threshold of chaos occurrence. By fine-tuning the system parameters, a criterion for designing the control parameters to make the Melnikov function non-zero is derived. In addition, the routes to chaos in controlled system are explored by bifurcation diagrams, largest Lyapunov exponents, phase portraits, Poincar & eacute; maps, basins of attraction, frequency spectra, and displacement time series. The results indicate that by properly adjusting the displacement feedback coefficient and the amplitude of parameter excitation, the chaotic motion caused by increasing of the amplitude of external excitation and strength of distributed time delay can be effectively suppressed. This research result can provide theoretical support for exploring the potential chaotic motion of other types of oscillators.
Keyword ：
active control active control pitchfork bifurcation pitchfork bifurcation mixed Rayleigh-Li & eacute;nard oscillator mixed Rayleigh-Li & eacute;nard oscillator Melnikov method Melnikov method chaos chaos
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| GB/T 7714 | Zhao, Hongzhen , Li, Jing , Zhu, Shaotao et al. Bifurcation and Chaos Control of Mixed Rayleigh-LiéNard Oscillator With Two Periodic Excitations and Mixed Delays [J]. | MATHEMATICAL METHODS IN THE APPLIED SCIENCES , 2025 , 48 (5) : 5586-5601 . |
| MLA | Zhao, Hongzhen et al. "Bifurcation and Chaos Control of Mixed Rayleigh-LiéNard Oscillator With Two Periodic Excitations and Mixed Delays" . | MATHEMATICAL METHODS IN THE APPLIED SCIENCES 48 . 5 (2025) : 5586-5601 . |
| APA | Zhao, Hongzhen , Li, Jing , Zhu, Shaotao , Zhang, Yufeng , Sun, Bo . Bifurcation and Chaos Control of Mixed Rayleigh-LiéNard Oscillator With Two Periodic Excitations and Mixed Delays . | MATHEMATICAL METHODS IN THE APPLIED SCIENCES , 2025 , 48 (5) , 5586-5601 . |
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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 ：
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 ：
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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