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Abstract During the construction of deep vertical shafts, water inrush and flooding accidents are prone to occur, which seriously affect construction safety. Accurately determining the groundwater conditions is a prerequisite for effectively controlling water hazards and conducting risk management. In order to ensure the accuracy of the resistivity method in deep vertical well water exploration construction, a combination of indoor rock physics, mechanical testing, and on-site engineering measurements was used to analyze the influencing factors of granite resistivity. The corresponding relationship between resistivity and formation integrity was revealed, and water exploration experiments were conducted in the working face of deep underground mines. The results show that: (1) Rock resistivity is influenced by metallic minerals, saturation, temperature, ion content of fracture water, and joints. Regarding deep subsurface detection issues, the main factors affecting the detection results are water content and rock integrity. (2) During the loading process, rock resistivity exhibits significant stage response characteristics, which are closely related to rock integrity and damage accumulation. (3) A degradation model for aquifer zoning based on resistivity benchmark line was established. When the formation resistivity is higher than the benchmark line, it indicates a well-integrated formation with low water content. (4) Resistivity cloud maps and zoning degradation models can be used to visually determine and evaluate the occurrence status of formations and the effectiveness of grouting.

Three models for the propagation of forest disease are revisited to include the effect of forest fires and disease spread. We study the global stability of the forest-disease model in the absence of forest fires and the spread of disease. When forest fires caused by grass cover are considered, we show that the equilibrium points are locally asymptotically stable. If both forest fires and the spread of disease exist in the second model, then Turing instability can occur. In this case, the system exhibits complex dynamic behavior. To determine the effect of fire on the forest disease model, we obtain the optimal control expression of the key parameter fire factor, and carry out sensitivity analysis. Finally, we use forest biomass data of some provinces in China from 2002 to 2018 for numerical simulation, and the results are in agreement with the theoretical analysis.

Abstract The unique dumbbell-shape of grass guard cells (GCs) is controlled by their cell walls which enable their rapid responses to the environment. The molecular mechanisms regulating the synthesis and assembly of GC walls are as yet unknown. Here we have identified BZU3, a maize gene encoding UDP-glucose 4-epimerase that regulates the supply of UDP-glucose during GC wall synthesis. The BZU3 mutation leads to significant decreases in cellular UDP-glucose levels. Immunofluorescence intensities reporting levels of cellulose and mixed-linkage glucans are reduced in the GCs, resulting in impaired local wall thickening. BZU3 also catalyzes the epimerization of UDP-N-acetylgalactosamine to UDP-N-acetylglucosamine, and the BZU3 mutation affects N-glycosylation of proteins that may be involved in cell wall synthesis and signaling. Our results suggest that the spatiotemporal modulation of BZU3 plays a dual role in controlling cell wall synthesis and glycosylation via controlling UDP-glucose/N-acetylglucosamine homeostasis during stomatal morphogenesis. These findings provide insights into the mechanisms controlling formation of the unique morphology of grass stomata.

This paper examines the dynamic behavior of a particular category of discrete predator-prey system that feature both fear effect and refuge, using both analytical and numerical methods. The critical coefficients and properties of bifurcating periodic solutions for Flip and Hopf bifurcations are computed using the center manifold theorem and bifurcation theory. Additionally, numerical simulations are employed to illustrate the bifurcation phenomenon and chaos characteristics. The results demonstrate that period-doubling and Hopf bifurcations are two typical routes to generate chaos, as evidenced by the calculation of the maximum Lyapunov exponents near the critical bifurcation points. Finally, a feedback control method is suggested, utilizing feedback of system states and perturbation of feedback parameters, to efficiently manage the bifurcations and chaotic attractors of the discrete predator-prey model.

Background. Growing evidence has revealed that m6A modification of long noncoding RNAs (lncRNAs) dynamically controls tumor stemness and tumorigenesis-related processes. However, the prognostic significance of m6A-related lncRNAs and their associations with stemness in low-grade glioma (LGG) remain to be clarified. Methods. A multicenter transcriptome analysis of lncRNA expression in 1,247 LGG samples was performed in this study. The stemness landscape of LGG tumors was presented and associations with clinical features were revealed. The m6A-related lncRNAs were identified between stemness groups and were further prioritized via least absolute shrinkage and selection operator Cox regression analysis. A risk score model based on m6A-related lncRNAs was constructed and validated in external LGG datasets. Results. Based on the expression of LINC02984, PFKP-DT, and CRNDE, a risk model and nomogram were constructed; they successfully predicted the survival of patients and were extended to external datasets. Significant correlations were observed between the risk score and tumor stemness. Moreover, patients in different risk groups exhibited distinct tumor immune microenvironments and immune signatures. We finally provided several potential compounds suitable for specific risk groups, which may aid in LGG treatment. Conclusions. This novel signature presents noteworthy value in the prediction of prognosis and stemness status for LGG patients and will foster future research on the development of clinical regimens.

In this paper, the dynamical behavior of a predator-prey model with discrete time is discussed in terms of both theoretical analysis and numerical simulation. The existence and stability of four equilibria are analyzed. It is proved that the system undergoes Flip bifurcation and Hopf bifurcation around its unique positive equilibrium point using center manifold theorem and bifurcation theory. Additionally, by applying small perturbations to the bifurcation parameter, chaotic cases occur at some corresponding internal equilibria. Finally, numerical simulations are provided with the help of maximum Lyapunov exponent and phase diagrams, which reveal a complex dynamical behavior.

In this paper, we study the general mechanism of Turing-pattern in a tree-grass competition model with cross diffusion and time delay. The properties of four equilibrium points, the existence of Hopf bifurcation and the sufficient conditions for Turing instability caused by cross-diffusion are analyzed, respectively. The amplitude equation of tree-grass competition model is derived by using multi-scale analysis method, and its nonlinear stability is studied. The sensitivity analysis also verified that fire frequency plays a key role in tree-grass coexistence equilibrium. Finally, the Turing pattern of tree-grass model obtained by numerical simulation is consistent with the spatial structure of tree-grass density distribution observed in Hulunbuir grassland, China.

The Turing patterns of reaction-diffusion equations defined over a square region are more complex because of the D4-symmetry of the spatial region. This leads to the occurrence of multiple equivariant Turing bifurcations. In this paper, taking the FHN model as an example, we give a explicit calculation formula of normal form for the simple and double Turing bifurcation of the reaction-diffusion equation with Dirichlet boundary conditions and defined on a square space, and we also obtain a method for the calculation of the existence of spatially inhomogeneous steady-state solutions. This paper provides a theoretical basis for exploring and predicting the pattern formation of spatial multimode interaction.

This paper considers the influence of cross-diffusion on semi-arid ecosystems based on simplified Hardenberg's reaction diffusion model. In the square region, we analyze the properties of this model and give the relaxation time correspond to the system to prejudge the approximate time of this system stabilization process. The numerical results are constant with the theory very well.

Cybersecurity faces constant challenges from increasingly sophisticated network attacks. Recent research shows machine learning can improve attack detection by training models on large labeled datasets. However, obtaining sufficient labeled data is difficult for internal networks. We propose a deep transfer learning model to learn common knowledge from domains with different features and distributions. The model has two feature projection networks to transform heterogeneous features into a common space, and a classification network then predicts transformed features into labels. To align probability distributions for two domains, maximum mean discrepancy (MMD) is used to compute distribution distance alongside classification loss. Though the target domain only has a few labeled samples, unlabeled samples are adequate for computing MMD to align unconditional distributions. In addition, we apply a soft classification scheme on unlabeled data to compute MMD over classes to further align conditional distributions. Experiments between NSL-KDD, UNSW-NB15, and CICIDS2017 validate that the method substantially improves cross-domain network attack detection accuracy.

In this paper, a system of four coupled van der Pol oscillators with delay is studied. Firstly, the conditions for the existence of multiple periodic solutions of the system are given. Secondly, the multiple periodic solutions of spatiotemporal patterns of the system are obtained by using symmetric Hopf bifurcation theory. The normal form of the system on the central manifold and the bifurcation direction of the bifurcating periodic solutions are derived. Finally, numerical simulations are attached to demonstrate our theoretical results.

In this paper, we consider a general time-space discrete host-parasitoid model with the periodic boundary conditions. We analyzed and obtained some usual conditions, such as Turing instability occurrence, Flip bifurcation occurrence, and Neimark-Sacker bifurcation occurrence. We also find several multiple bifurcation phenomena, such as 1 : 2 Resonance, Neimark-Sacker-Flip bifurcation, Neimark-Sacker-Neimark-Sacker bifurcation, Neimark-Sacker-Flip-Flip bifurcation, induced by diffusion. In a modified Nicholson-Bailey model, employing the mutual interference and diffusive interaction as bifurcation parameters, there appear route from standing Turing instability to multiple bifurcations by changing diffusive parameters. Some numerical simulations of the modified Nicholson-Bailey model support these corollaries.

In this paper, we extend a Leslie–Gower-type predator–prey system with ratio-dependent Holling III functional response considering the cost of antipredator defence due to fear. We study the impact of the fear effect on the model, and we find that many interesting dynamical properties of the model can occur when the fear effect is present. Firstly, the relationship between the fear coefficient K and the positive equilibrium point is introduced. Meanwhile, the existence of the Turing instability, the Hopf bifurcation, and the Turing–Hopf bifurcation are analyzed by some key bifurcation parameters. Next, a normal form for the Turing–Hopf bifurcation is calculated. Finally, numerical simulations are carried out to corroborate our theoretical results.

In this paper, we deduce a predator–prey model with discrete time in the interior of R+2 using a new discrete method to study its local dynamics and Neimark–Sacker bifurcation. Compared with continuous models, discrete ones have many unique properties that help to understand the changing patterns of biological populations from a completely new perspective. The existence and stability of the three equilibria are analyzed, and the formation conditions of Neimark–Sacker bifurcation around the unique positive equilibrium point are established using the center manifold theorem and bifurcation theory. An attracting closed invariant curve appears, which corresponds to the periodic oscillations between predators and prey over a long period of time. Finally, some numerical simulations and their biological meanings are given to reveal the complex dynamical behavior.

Unruptured intracranial aneurysm (UIA) is a life-threatening cerebrovascular condition. Here the authors report altered gut microbiota including low abundance of Hungatella hathewayi in patients with UIAs, and show that supplementation with Hungatella hathewayi or the metabolite taurine prevents UIAs in mice.

In this paper, Van Der Pol (VDP) oscillators are used as the output signal of central pattern generator (CPG), and a VDP-CPG network system of quadruped with four primary gaits (walk, trot, pace and bound) is established. The existence conditions of Hopf bifurcations for VDP-CPG systems corresponding to four primary gaits are given, and the coupling strength ranges between oscillators for four gaits are obtained. Numerical simulations are used to support theoretical analysis.

On the basis of logistic models of forest restoration, we consider the influence of population pressure on forest restoration and establish a reaction diffusion model with Holling II functional responses. We study this reaction diffusion model under Dirichlet boundary conditions and obtain a positive equilibrium. In the square region, we analyze the existence of Turing instability and Hopf bifurcation near this point. The square patterns and mixed patterns are obtained when steady-state bifurcation occurs, the hyperhexagonal patterns appears in Hopf bifurcation.

This paper is concerned with how the singularity and delay in a feed forward neural network affect generic dynamics and bifurcations. By computation of Hopf-pitchfork point in a two-parameter nonlinear problem, the mode interactions in two parameters bifurcations with a single zero and a pair of imaginary roots are considered. The codimension two normal form with Hopf-pitchfork bifurcations are given. Then, the bifurcation diagrams and phase portraits are obtained by computing the normal form. Furthermore, we find some interesting dynamical behaviors of the original system, such as the coexistence of two unstable nontrivial equilibria and a pair of stable periodic orbits, which are verified both theoretically and numerically. Through numerical simulation, we also find that this model has a special signal enhancement property in Hopf bifurcation state. Using this feed-forward neural network, we show that the gray scale picture contrast is strongly enhanced even if this one is initially very small.

Affected by faults, fractures, and high ground stress, the deep shaft wall is prone to deformation and fracture, which affects the safety of mine construction. To investigate the stress and deformation of the shaft wall at the horsehead gate connection, the force-measuring bolt and vibrating string concrete strain gauges were installed for on-site monitoring prior to the shaft wall pouring. It was found that the concrete strains and forces on the shaft wall were divided into four stages during the tedious shaft construction. The measured data showed that the maximum pressure and tension on the shaft wall were 4.5 MPa and 1.3 MPa, respectively, the maximum axial compressive and tensile strains were -500 με and 1700 με, and the maximum circumferential compressive and tensile strains were -1000 με and 400 με. During the shaft excavation construction, there is a tensile state in the shaft wall at the connection of the horsehead gate. In addition, there will be uneven stress in the concrete support structure and a sharp increase in the local stress of the shaft wall. Therefore, the problem of supporting the wall of deep shafts is undoubtedly a significant challenge in the construction of shafts. The numerical simulation results combined with the on-site monitoring of the layers show that stress concentrations occur at the lower end of the shaft wall and the interconnections between the walls during the excavation process. Therefore, it is essential to pay attention to the stress values in the lower part of the wall when constructing deeper sections to avoid stress concentrations and pay attention to the construction quality when constructing the wall joints to meet the wall’s safety needs support.

Non-noble-metal-based chalcogenides are promising candidates for hydrogen evolution reaction (HER) by harnessing the architectural design and the synergistic effect between the elements. Herein, a porous bimetallic selenide (NiFeSe) nanocube deposited on carbon fiber paper (NiFeSe/CFP) was synthesized through a facile selenization reaction based on Prussian blue analogues (PBAs) as precursors. The NiFeSe/CFP exhibited excellent HER activity with an overpotential of just 186 mV for a current density of 10 mA cm−2 in 1.0 M KOH at ambient temperature, similar to most of the state-of-the-art transition metal chalcogenides. The corresponding Tafel slope was calculated to be 52 mV dec−1, indicating fast discharge of the proton during the HER. Furthermore, the catalyst could endure long-term catalytic tests and showed remarkable durability. The enhanced electrocatalytic performance of NiFeSe/CFP is attributed to the unique 3D porous configuration inherited from the PBA templates, enhanced charge transfer occurring at the heterogeneous interface due to the synergistic effect between the bimetallic phases, and the high conductivity improved by the formation of amorphous carbon shells during the selenization. These findings prove that the combination of inexpensive metal–organic framework precursors and hybrid metallic compounds is a feasible way to realize the performance enhancement of non-noble-metal-based chalcogenides towards alkaline HER.

In this article, we propose a mathematical model for insect outbreaks coupled with wildfire disturbances and an optimization model for finding suitable wildfire frequencies. We use a refined Holling II function as a model for the nonlinear response of fire frequency against trees and insects. The results show that for the tree–insect–wildfire model, there is a coexistence equilibrium in the system. Sensitivity analysis is performed to determine the effect of wildfire on trees in the optimization model. The results show that forest fires have a significant impact on the equilibrium mechanism of tree–insect coexistence. Numerical simulations suggest that in some areas of high fire intensity, there may be positive feedback between disturbances from wildfires and insect outbreaks. The result is consistent with the present theory in this field.

In this paper, the Hopf-zero bifurcation of the ring unidirectionally coupled Toda oscillators with delay was explored. First, the conditions of the occurrence of Hopf-zero bifurcation were obtained by analyzing the distribution of eigenvalues in correspondence to linearization. Second, the stability of Hopf-zero bifurcation periodic solutions was determined based on the discussion of the normal form of the system, and some numerical simulations were employed to illustrate the results of this study. Lastly, the normal form of the system on the center manifold was derived by using the center manifold theorem and normal form method.

Autophagy is a self-degradation process that maintains homeostasis against stress in cells. Autophagy dysfunction plays a central role in the development of tumors, such as colorectal cancer (CRC). In this study, autophagy-related differentially expressed genes, their downstream functions, and upstream regulatory factors including RNA-binding proteins (RBP) involved in programmed cell death in the CRC were investigated. Transcription factors (TFs) and miRNAs have been shown to mainly regulate autophagy genes. Interestingly, we found that some of the RBP in the CRC, such as DDX17, SETDB1, and POLR3A, play an important regulatory role in maintaining autophagy at a basal level during growth by acting as TFs that regulate autophagy. Promoter methylations showed negative regulations on differentially expressed autophagy gene (DEAG), while copy number variations revealed a positive role in them. A proportional hazards regression analysis indicated that using autophagy-related prognostic signature can divide patients into high-risk and low-risk groups. Autophagy associated FDA-approved drugs were studied by a prognostic network. This would contribute to the identifications of new potential molecular therapeutic targets for CRC.

The wheel-side direct-driven transmission system (WDTS) is a new intelligent transmission technology, which has significant advantages in high-efficiency and few malfunctions for the electric bus. Based on the Lagrange–Maxwell equation, the WDTS electromechanical coupling dynamic model, whose effectiveness is verified by the PMSM speed, is constructed for analyzing the system torsional vibration destabilization characteristics. Then, by determining the resonance curve equation for the torsional vibration response amplitude of the WDTS with the direct multi-scale method, the influences of the torque ripple amplitude of the PMSM and the transmission clearance on the system torsional vibration stability are analyzed. The results indicate that the WDTS torsional vibration response shows complex nonlinear characteristics especially under the effect of the system transmission clearance, which has an important impact on the system stable operation. The research results can lay a theoretical foundation for the design of the WDTS of the electric bus.

Abstract In this paper, we study the Hopf-zero bifurcation of Oregonator oscillator with delay. The interaction coefficient and time delay are taken as two bifurcation parameters. Firstly, we get the normal form by performing a center manifold reduction and using the normal form theory developed by Faria and Magalhães. Secondly, we obtain a critical value to predict the bifurcation diagrams and phase portraits. Under some conditions, saddle-node bifurcation and pitchfork bifurcation occur along M and N, respectively; Hopf bifurcation and heteroclinic bifurcation occur along H and S, respectively. Finally, we use numerical simulations to support theoretical analysis.

Abstract In this paper, we consider a modified predator–prey model with Michaelis–Menten-type predator harvesting and diffusion term. We give sufficient conditions to ensure that the coexisting equilibrium is asymptotically stable by analyzing the distribution of characteristic roots. We also study the Turing instability of the coexisting equilibrium. In addition, we use the natural growth rate r1 $r_{1}$ of the prey as a parameter and carry on Hopf bifurcation analysis including the existence of Hopf bifurcation, bifurcation direction, and the stability of the bifurcating periodic solution by the theory of normal form and center manifold method. Our results suggest that the diffusion term is important for the study of the predator–prey model, since it can induce Turing instability and spatially inhomogeneous periodic solutions. The natural growth rate r1 $r_{1}$ of the prey can also affect the stability of positive equilibrium and induce Hopf bifurcation.

Users of social networks have a variety of social statuses and roles. For example, the users of Weibo include celebrities, government officials, and social organizations. At the same time, these users may be senior managers, middle managers, or workers in companies. Previous studies on this topic have mainly focused on using the categorical, textual and topological data of a social network to predict users’ social statuses and roles. However, this cannot fully reflect the overall characteristics of users’ social statuses and roles in a social network. In this paper, we consider what social network structures reflect users’ social statuses and roles since social networks are designed to connect people. Taking an Enron email dataset as an example, we analyzed a preprocessing mechanism used for social network datasets that can extract users’ dynamic behavior features. We further designed a novel social network representation learning algorithm in order to infer users’ social statuses and roles in social networks through the use of an attention and gate mechanism on users’ neighbors. The extensive experimental results gained from four publicly available datasets indicate that our solution achieves an average accuracy improvement of 2% compared with GraphSAGE-Mean, which is the best applicable inductive representation learning method.

The actuator of a particleboard glue-dosing system, the glue pump motor, is affected by external disturbances and unknown uncertainty. In order to achieve accurate glue-flow tracking, in this paper, a glue pump motor compound control method was designed. First, the prescribed performance control method is used to improve the transient behaviors, and the error of the glue flow tracking is guaranteed to converge to a preset range, as a result of the design of an appropriate performance function. Second, two extended state observers were designed to estimate the state vector and the disturbance, in order to improve the robustness of the controlled system. To further strengthen the steady-state performance of the system, the sliding-mode dynamic surface control method was introduced to compensate for uncertainties and disturbances. Finally, a Lyapunov stability analysis was conducted, in order to prove that all of the signals are bounded in a closed-loop system, and the effectiveness and feasibility of the proposed method were verified through numerical simulation.

The elastic vibration of the flexible manipulator is the key problem to be solved before its effective application. The mobile flexible manipulator system (MFMS), under variable load conditions, is taken as the research object. Based on Lagrange’s principle and the singular perturbation theory, the two-timescale subsystems dynamic models of the MFMS are constructed to set up the system payment function and the Hamiltonian function which correspond to the subsystems states and errors. Then, with the minimization of the system Hamiltonian function, the synchronization optimization of the designed two-timescale optimal observer (TSOO) and the designed optimal state feedback controller is realized, under the premise of the system stability which is verified by the Lyapunov stability criterion. Furthermore, with the contradiction between the control rapidity and the accuracy of the optimal state feedback controller considered, by combining the input shaping technology, the master-slave composite controller for the elastic vibration of the MFMS is constructed. Finally, simulation results verify the validity of the designed TSOO and the master-slave composite controller.

The problem of the elastic vibration control for a translational flexible manipulator system (TFMS) under variable load conditions is studied. The input shaper can effectively filter out the vibration excitation components for the flexible manipulator in the driving signals, but the adaptability and rapidity of the conventional input shaper are poor because it is essentially an open-loop control mode and there are time-lag links inevitably. Thus, by combining the state feedback with the input shaping, a master-slave integrated controller of the TFMS is proposed. Moreover, in order to solve the time-lag effect of the conventional input shaper, based on the optimal algorithm, a two-mode vibration cascade shaper for the TFMS is designed. Then, under variable load conditions, the control effects of the conventional input shapers, the two-mode vibration cascade shaper, and the combination of the state feedback integral controller (SFIC) with the above shapers are investigated. The results show that the designed master-slave integrated controller has high robustness under variable load conditions and takes good account of the requirements of system response time and overshoot for achieving the goal of nonovershoot under fast response speed. Simulation experiment results verify the effectiveness of the designed controller.

WRKY proteins are a large family of transcription factors that are involved in diverse developmental processes and abiotic stress responses in plants. However, our knowledge of the regulatory mechanisms of WRKYs participation in protein–protein interactions is still fragmentary, and such protein–protein interactions are fundamental in understanding biological networks and the functions of proteins. In this study, we report that a WRKY protein from Tamarix hispida, ThWRKY4, can form both homodimers and heterodimers with ThWRKY2 and ThWRKY3. In addition, ThWRKY2 and ThWRKY3 can both bind to W-box motif with binding affinities similar to that of ThWRKY4. Further, the expression patterns of ThWRKY2 and ThWRKY3 are similar to that of ThWRKY4 when plants are exposed to abscisic acid (ABA). Subcellular localization shows that these three ThWRKY proteins are nuclear proteins. Taken together, these results demonstrate that ThWRKY4 is a dimeric protein that can form functional homodimers or heterodimers that are involved in abiotic stress responses.

Gibberellin (GA) is a key signal molecule inducing differentiation of tracheary elements, fibers, and xylogenesis. However the molecular mechanisms underlying the effect of GA on xylem elongation and secondary wall development in tree species remain to be determined. In this study, Betula platyphylla (birch) seeds were treated with 300 ppm GA3 and/or 300 ppm paclobutrazol (PAC), seed germination was recorded, and transverse sections of hypocotyls were stained with toluidine blue; the two-month-old seedlings were treated with 50 μM GA3 and/or 50 μM PAC, transverse sections of seedling stems were stained using phloroglucinol–HCl, and secondary wall biosynthesis related genes expression was analyzed by real-time quantitative PCR. Results indicated that germination percentage, energy and time of seeds, hypocotyl height and seedling fresh weight were enhanced by GA3, and reduced by PAC; the xylem development was wider in GA3-treated plants than in the control; the expression of NAC and MYB transcription factors, CESA, PAL, and GA oxidase was up-regulated during GA3 treatment, suggesting their role in GA3-induced xylem development in the birch. Our results suggest that GA3 induces the expression of secondary wall biosynthesis related genes to trigger xylogenesis in the birch plants.

In this paper, the Hopf-pitchfork bifurcation of coupled van der Pol with delay is studied. The interaction coefficient and time delay are taken as two bifurcation parameters. Firstly, the normal form is gotten by performing a center manifold reduction and using the normal form theory developed by Faria and Magalhães. Secondly, bifurcation diagrams and phase portraits are given through analyzing the unfolding structure. Finally, numerical simulations are used to support theoretical analysis.

In order to eliminate the influence of the joint torsional vibration on the system operation accuracy, the parameter identification and the elastic torsional vibration control of a flexible-joint robot are studied. Firstly, the flexible-joint robot system is equivalent to a rotor dynamic system, in which the mass block and the torsion spring are used to simulate the system inertia link and elasticity link, for establishing the system dynamic model, and the experimental prototype is constructed. Then, based on the mechanism method, the global electromechanical-coupling dynamic model of the flexible-joint robot system is constructed to clear and define the mapping relationship between the driving voltage of the DC motor and the rotational speed of joint I and joint II. Furthermore, in view of the contradiction between the system response speed and the system overshoot in the vibration suppression effect of the conventional PID controller, a fuzzy PID controller, whose parameters are determined by the different requirements in the vibration control process, is designed to adjust the driving voltage of the DC motor for attenuating the system torsional vibration. Finally, simulation and control experiments are carried out and the results show that the designed fuzzy PID controller can effectively suppress the elastic torsional vibration of the flexible-joint robot system with synchronization optimization of control accuracy and dynamic quality.

In the process of particleboard glue mixing and dosing control under the working condition of intermediate frequency, a sliding-mode dynamic surface control strategy based on high-gain observer is proposed in this paper to deal with the problem of glue flow stability caused by strong nonlinearity. The high-gain observer (HGO) is aimed at estimating the derivative of the immeasurable system input signal for feedback, and the robustness of the system is improved by the dynamic surface control (DSC) method. Furthermore, the sliding-mode control (SMC) method is used to deal with disturbances caused by the uncertainties as well as external disturbances. It is proven that the system is exponential asymptotic stable by constructing a suitable Lyapunov function. Simulation results show that the proposed control methods can make the system track the expected flow value quickly and accurately. Finally, numerical simulation results are exhibited to authenticate and validate the effectiveness of the proposed control scheme.

This work explores a coupled Oregonator model. By analyzing the associated characteristic equation, linear stability is investigated and Hopf bifurcations are demonstrated, as well as the stability and direction of the Hopf bifurcation are determined by employing the normal form method and the center manifold reduction. We also discussed the Z2 equivariant property and the existence of multiple periodic solutions. Numerical simulations are presented to illustrate the results in Section 5.

In this paper, the problem of the stability for mutually delay-coupled semiconductor lasers system is investigated. By analyzing the associated characteristic equation, linear stability is investigated and Hopf bifurcations are demonstrated. The new phenomena such as stability switch is found. The Z2 equivariant property and the existence of multiple periodic solutions is also discussed. Numerical simulations are presented to illustrate the results in the paper.

We establish some algebraic results on the zeros of some exponential polynomials and a real coefficient polynomial. Based on the basic theorem, we develop a decomposition technique to investigate the stability of two coupled systems and their discrete versions, that is, to find conditions under which all zeros of the exponential polynomials have negative real parts and the moduli of all roots of a real coefficient polynomial are less than 1.

We analyze a differential-algebraic biological economic system with time delay. The model has two different Holling functional responses. By considering time delay as bifurcation parameter, we find that there exists stability switches when delay varies, and the Hopf bifurcation occurs when delay passes through a sequence of critical values. Furthermore, we also consider the stability and direction of the Hopf bifurcation by applying the normal form theory and the center manifold theorem. Finally, using Matlab software, we do some numerical simulations to illustrate the effectiveness of our results.

The eigenvalues and the stability of a singular neutral differential system with single delay are considered. Firstly, by applying the matrix pencil and the linear operator methods, new algebraic criteria for the imaginary axis eigenvalue are derived. Second, practical checkable criteria for the asymptotic stability are introduced.

Dynamic properties are investigated in the coupled system of three maps with symmetric nearest neighbor coupling and periodic boundary conditions. The dynamics of the system is controlled by certain coupling parameters. We show that, for some values of the parameters, the system exhibits nontrivial collective behavior, such as multiple bifurcations, and chaos. We give computer simulations to support the theoretical predictions.