Jing Li

• Professor
• Beijing University of Technology

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 orbit...

This paper investigates the bifurcation, chaos, and active control of a mixed Rayleigh‐Liénard 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...

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 t...

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...

Purpose The main purpose of this study is to analyze the heat transfer phenomena in a dynamically bulging enclosure filled with Cu-water nanofluid. This study examines the convective heat transfer process induced by a bulging area considered a heat source, with the enclosure's side walls having a low temperature and top and bottom walls being treat...

In this paper, we propose and study a discretized one‐predator two‐prey system along with prey refuge and Michaelis–Menten‐type prey harvesting. The interaction among the species is considered as Holling type III functional response. Firstly, existence and local stability of all the fixed points are derived under certain parametric conditions. Furt...

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 $${\textbf{R}}^{m+4}$$ R m + 4 , where m represents any positive integer. The extended Melnikov function is obtained by constructing a Poincaré map on the curviline...

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 re...

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 ∏A(KA+...

This paper propose a grounded-type DVA attached to a damped primary system, which can effectively suppress the vibration amplitudes by introducing a lever, focusing on the optimal design of the novel DVA. It can be utilized to the simplified model of a damped spacecraft or stay cable of cable-stayed bridges. The design of DVA considers \({\mathrm{H...

Carbon fiber reinforced polymer is a composite material, which is widely used in various engineering fields due to its excellent properties. We systematically discuss the influence of axial load amplitude parameters on the multiple periodic motions of carbon fiber reinforced polymer laminated cylindrical shell model. Based on the Melnikov vector fu...

In this paper, the Casson fluid model and the inclined magnetic field are used to analyse mathematically the energy transport of double diffusive natural convection (DDNC) in a curvilinear enclosure. The Galerkin finite element method (GFEM) is used to discretize the equations. When simulating the different ranges of Rayleigh numbers (10 ⁵ ≤ Ra ≤ 1...

This paper analytically and numerically investigates the dynamical characteristics of a fractional Duffing–van der Pol oscillator with two periodic excitations and the distributed time delay. First, we consider the pitchfork bifurcation of the system driven by both a high-frequency parametric excitation and a low-frequency external excitation. Util...

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-fre...

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∞ optimization problem of a novel three-elemen...

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 o...

Fractional q-calculus plays an extremely important role in mathematics and physics. In this paper, we aim to investigate the existence of triple-positive solutions for nonlinear singular fractional q-difference equation boundary value problems at resonance by means of the fixed-point index theorem and the q-Laplace transform, where the nonlinearity...

Due to the great application potential of fractional q-difference system in physics, mechanics and aerodynamics, it is very necessary to study fractional q-difference system. The main purpose of this paper is to investigate the solvability of nonlinear fractional q-integro-difference system with the nonlocal boundary conditions involving diverse fr...

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...

Chirality is an indispensable geometric property in the world that has become invariably interlocked with life. The main goal of this paper is to study the nonlinear dynamic behavior and periodic vibration characteristic of a two-coupled-oscillator model in the optics of chiral molecules. We systematically discuss the stability and local dynamic be...

A novel dynamic vibration absorber(DVA) model with negative stiffness and inerter-mass is presented and analytically studied in this paper. The research shows there are still two fixed points independent of the absorber damping in the amplitude frequency curve of the primary system when the system contains negative stiffness and inerter-mass. The o...

In this paper, we focus on the multiple periodic vibration behaviors of an auxetic honeycomb sandwich plate subjected to in-plane and transverse excitations. Nonlinear equation of motion for the plate is derived based on the third-order shear deformation theory and von Kármán type nonlinear geometric assumptions. The Melnikov method is extended to...

Q-calculus plays an extremely important role in mathematics and physics, especially in quantum physics, spectral analysis and dynamical systems. In recent years, many scholars are committed to the research of nonlinear quantum difference equations. However, there are few works about the nonlinear $ q- $difference equations with $ p $-Laplacian. In...

In this paper, by seeking the zero and the positive entry positions of the solution, we provide a direct method, called the reduced order method, for solving the linear complementarity problem with an M -matrix. By this method, the linear complementarity problem is transformed into a low order linear complementarity problem with some low order line...

The research gradually highlights vibration and dynamical analysis of symmetric coupled nonlinear oscillators model with clearance. The aim of this paper is the bifurcation analysis of the symmetric coupled nonlinear oscillators modeled by a four-dimensional nonsmooth system. The approximate solution of this system is obtained with aid of averaging...

Ring truss antenna is an ideal structure for large satellite antenna, which can be equivalent to circular cylindrical shell model. Based on the high-dimensional nonlinear dynamic vibration and bifurcation theory, we focus on the nonlinear dynamic behavior for breathing vibration system of ring truss antenna with internal resonance. The nonlinear tr...

We consider the negative order KdV (NKdV) hierarchy which generates nonlinear integrable equations. Selecting different seed functions produces different evolution equations. We apply the traveling wave setting to study one of these equations. Assuming a particular type of solution leads us to solve a cubic equation. New solutions are found, but no...

Nowadays, many researches have considerable attention to the nonlinear q-difference equations boundary value problems as important and useful tool for modeling of different phenomena in various research fields. In this work, we investigate a class of q-difference equations boundary value problems with integral boundary conditions with p-Laplacian o...

In high dimension, the bifurcation theory of periodic orbits of nonlinear dynamics systems are difficult to establish in general. In this paper, by performing the curvilinear coordinate frame and constructing a Poincaré map, we obtain some sufficient conditions of the bifurcation of periodic solutions of some 2n-dimensional systems for the unpertur...

Normal form theory is a powerful tool for local bifurcation analysis of nonlinear dynamical systems. In this paper, we present the hypernormal form for a class of four-dimensional nonlinear smooth map under the near identity formal transformation, and derive the explicit formulas for the normal form coefficients associated with the original smooth...

Tourism is one of the largest and fastest developing industries in the world. As most protected areas have the purpose of both nature conservation and providing recreational opportunities, national parks and a variety of protected areas have become popular destinations for tourists worldwide. This paper critiques the appropriateness of current tour...

Large-scale deployable space spacecraft structures have a very wide range of appli-cations in the field of spaceflight. The main goal of this study is to investigate the maximum number of periodic solutions for a four-dimensional deployable circular mesh antenna model. We study the parameter conditions and upper bound of the number of periodic solu...

In this paper, the bifurcation of periodic solutions for a four-dimensional cubic nonlinear dynamic system with a center singular point in resonance 1:1 and its application are investigated. The existence of periodic solutions bifurcating from the resonant center is obtained by introducing variables transformation and defining Poincare map. The res...

In this paper, we study the bifurcation of periodic solutions for a four-dimensional deployable circular mesh antenna system. The tools for proving these results are the averaging theory and Brouwer degree theory. Based on constructing displacement maps, we study the bifurcation of the periodic solutions of linear center, and to discuss the maximum...

In this paper, the bifurcations and chaos dynamics of a hyperjerk system with antimonotonicity are investigated via the analytical methods and numerical calculations. We discuss the local stabilities of equilibrium points and its bifurcations depending on parameters. The predicted bifurcations of periodic orbits including flip bifurcation, fold bif...

This paper is devoted to consider the existence and bifurcation of subharmonic solutions of two types of 2n-dimensional nonlinear systems with time-dependent perturbations. When the unperturbed system is a Hamiltonian system, we obtain the extended Melnikov function by means of performing the curvilinear coordinate frame and constructing a Poincaré...

In this paper, we are concerned with periodic motions of composite laminated circular cylindrical shell with 1:2 internal resonance. The existence condition and number estimation of periodic solutions of the governing system are studied by discussing the Poincaré map and the displacement function. To illustrate the effectiveness of our results, the...

In this paper, we focus on the two-coupled-oscillator model in optics chiral molecular medium. We perform scale transformations for variables and study the existence of periodic solutions in detail for the two-coupled-oscillator system. We obtain the Melnikov function by establishing the curvilinear coordinate transformation and constructing a Poin...

In this paper, the well-posedness for the non-autonomous reaction–diffusion equation with infinite delays on a bounded domain is established. The existence of pullback attractors for the process in Cγ,Lr(Ω) and Cγ,W1,r(Ω) is proved, respectively. The noncompact Kuratowski measure is applied to check the asymptotic compactness.

In this paper, we study the existence and bifurcation of subharmonic solutions of a four-dimensional slow–fast system with time-dependent perturbations for the unperturbed system in two cases: one is a Hamilton system and the other has a singular periodic orbit, respectively. We perform the curvilinear coordinate transformation and construct a Poin...

In this paper, we mainly focus on the unique normal form for a class of three-dimensional vector fields via the method of transformation with parameters. A general explicit recursive formula is derived to compute the higher order normal form and the associated coefficients, which can be achieved easily by symbolic calculations. To illustrate the ef...

In this paper, the unique normal form for a class of three-dimensional nilpotent vector fields with symmetry is investigated. The key technique used is a combination of multiple Lie brackets, linear grading function, new notations of block matrices and first integral of the linear part of the given vector field which avoids complicated calculations...

Four (2+1)-dimensional nonlinear evolution equations, generated by the Jaulent-Miodek hierarchy, are investigated by the bifurcation method of planar dynamical systems. The bifurcation regions in different subsets of the parameters space are obtained. According to the different phase portraits in different regions, we obtain kink (antikink) wave so...

We study the bifurcation of periodic solutions for viscoelastic belt with integral constitutive law in 1: 1 internal resonance. At the beginning, by applying the nonsingular linear transformation, the system is transformed into another system whose unperturbed system is composed of two planar systems: one is a Hamiltonian system and the other has a...

We present the unique normal form of a class of 3 dimensional vector fields (BT-zero singularity) with symmetries. The main technique applied to the computation is the combination of a linear grading function and the method of multiple Lie brackets. We introduce new notations for block matrices to simplify the expression of block matrices. The new...

In this paper we investigate the necessary condition for the existence of the periodic solution of honeycomb sandwich plate dynamic system of two-degree-of-freedom. We establish the curvilinear coordinates frame on closed orbits of the unperturbed system of the honeycomb sandwich plate dynamic system and construct successor function. Then we get th...

The stability and bifurcations of multiple limit cycles for the physical model of thermonuclear reaction in Tokamak are investigated in this paper. The one-dimensional Ginzburg-Landau type perturbed diffusion equations for the density of the plasma and the radial electric field near the plasma edge in Tokamak are established. First, the equations a...

Symbiosis is not only a biometric identification mechanism, but also a method of social science management. Symbiosis theory and other biometric theories are widely applied in social and economic researches. The paper research cycle of profits to the majority and minority shareholders in publicly listed companies based on mathematical model for qua...

Suspension cable structure is one of the most important structure. In this article the hypernormal form of icing suspension cable model with practical application background is investigated by using the method of New Grading Function and multi-lie bracket. First the average equations of icing suspension cable model is given, based on the equations,...

Honeycomb sandwich plate have been widly applied in industry design in recent years. In this paper, we study the cubic hypernormal form (the simplest normal form and the unique normal form) for honeycomb sandwich plate dynamics model with the help of Maple symbolic computation. Firstly, we get the average equation of four dimensional cartesian form...

To research hypernormal form (simplest normal form, unique normal form) of nilpotent three-dimensional vector fields, the problem of quintic hypernormal form of a class of nilpotent three-dimensional vector fields with symmetrical property was studied by using new grading function and the method of multiple Lie brackets and by introducing the new m...

In this paper, the periodic behavior of iced cable in the case of the in-plane fundamental parametric resonance-principal resonance, out-of-plane principal parametric resonance-principal resonance, and in 1:2 internal resonances is investigated. The sufficient condition for the existence of the periodic solutions about the system is obtained throug...

In this paper, the sufficient condition for the existence of periodic solution of a class of three dimensional nonlinear dynamical systems is investigated. The moving Frenet frame is established on the closed orbit and the successor functions near the closed orbit are defined. According to the study of the existence of solution of the equation whic...

In this paper, the average equations are given through using the multi-scale approach method. By using the Melinkov function, the nonsingular linear transformation and the Poincaré map, the sufficient condition for existence of periodic solution of the nonlinear dynamical system about the FGM subjected to aero-thermal load is derived.

In this paper, the peakons and bifurcations in a generalized Camassa-Holm equation are studied by using the bifurcation method and qualitative theory of dynamical systems. First, the averaged equation is obtained by introducing linear transform and traveling wave transform to the generalized Camassa-Holm equation. Then, we applied the bifurcation t...

In this paper, we investigate a class of three dimensional nonlinear dynamical systems whose unperturbed systems have a family of periodic orbits. Firstly, we establish the moving Frenet Frame on these closed orbits. Secondly, the successor functions are defined by the orbits which go through the normal plane. Finally, by judging the existence of s...

To research hypernormal form (simplest normal form, unique normal form) of nilpotent three-dimensional vector field, the authors obtained the first normal form of this system using normal form theory of ordinary differential equation and dynamical systems, and applying new grading function and the first integral of the linear part. With further red...

Based on wings flutter on flying aircraft in this paper, the authors study the mechanical model of the rectangular symmetric cross-ply composite laminated plates. Frist, the method of multiple scales is employed to obtain the four-dimensional averaged equations of the model. Then, the method of new grading function and multiple Lie brackets is util...

In this paper, the behavior of iced cable with two degrees of freedom is investigated. With Melnikov function of the system, the sufficient condition for the existence of periodic solutions about the system is obtained. The invariant tori of the system is investigated by using transformations and average equation. The conclusion not only enriches t...

With the development of science and technology, computer information technology has been widely applied in education and scientific research. In the process of teaching, properly using computer technology can effectively improve the teaching quality. This paper discusses some problems which Computer information technology was applied in mathematics...