Effects of viscoelasticity on the stability and bifurcations of nonlinear energy sinks

Due to the increasing use of passive absorbers to control unwanted vibrations,many studies have been done on energy absorbers ideally,but the lack of studies of real environmental conditions on these absorbers is felt.The present work investigates the effect of viscoelasticity on the stability and bifurcations of a system attached to a nonlinear energy sink(NES).In this paper,the Burgers model is assumed for the viscoelasticity in an NES,and a linear oscillator system is considered for investigating the instabilities and bifurcations.The equations of motion of the coupled system are solved by using the harmonic balance and pseudo-arc-length continuation methods.The results show that the viscoelasticity affects the frequency intervals of the Hopf and saddle-node branches,and by increasing the stiffness parameters of the viscoelasticity,the conditions of these branches occur in larger ranges of the external force amplitudes,and also reduce the frequency range of the branches.In addition,increasing the viscoelastic damping parameter has the potential to completely eliminate the instability of the system and gradually reduce the amplitude of the jump phenomenon.

Periodical Bifurcation Analysis of a Type of Hematopoietic Stem Cell Model with Feedback Control

The delay feedback control brings forth interesting periodical oscillation bifurcation phenomena which reflect in Mackey-Glass white blood cell model. Hopf bifurcation is analyzed and the transversal condition of Hopf bifurcation is given. Both the period-doubling bifurcation and saddle-node bifurcation of periodical solutions are computed since the observed floquet multiplier overpass the unit circle by DDE-Biftool software in Matlab. The continuation of saddle-node bifurcation line or period-doubling curve is carried out as varying free parameters and time delays. Two different transition modes of saddle-node bifurcation are discovered which is verified by numerical simulation work with aids of DDE-Biftool.

Bifurcation and dynamic response analysis of rotating blade excited by upstream vortices

A reduced model is proposed and analyzed for the simulation of vortexinduced vibrations （VIVs） for turbine blades. A rotating blade is modelled as a uniform cantilever beam, while a van der Pol oscillator is used to represent the time-varying characteristics of the vortex shedding, which interacts with the equations of motion for the blade to simulate the fluid-structure interaction. The action for the structural motion on the fluid is considered as a linear inertia coupling. The nonlinear characteristics for the dynamic responses are investigated with the multiple scale method, and the modulation equations are derived. The transition set consisting of the bifurcation set and the hystere- sis set is constructed by the singularity theory and the effects of the system parameters, such as the van der Pol damping. The coupling parameter on the equilibrium solutions is analyzed. The frequency-response curves are obtained, and the stabilities are determined by the Routh-Hurwitz criterion. The phenomena including the saddle-node and Hopf bifurcations are found to occur under certain parameter values. A direct numerical method is used to analyze the dynamic characteristics for the original system and verify the va- lidity of the multiple scale method. The results indicate that the new coupled model is useful in explaining the rich dynamic response characteristics such as possible bifurcation phenomena in the VIVs.

Bifurcation control of nonlinear oscillator in primary and secondary resonance

A weakly nonlinear oscillator was modeled by a sort of differential equation, a saddle-node bifurcation was found in case of primary and secondary resonance. To control the jumping phenomena and the unstable region of the nonlinear oscillator, feedback controllers were designed. Bifurcation control equations were obtained by using the multiple scales method. And through the numerical analysis, good controller could be obtained by changing the feedback control gain. Then a feasible way of further research of saddle-node bifurcation was provided. Finally, an example shows that the feedback control method applied to the hanging bridge system of gas turbine is doable.

Bifurcation and catastrophe of seepage flow system in broken rock

The study of dynamical behavior of water or gas flows in broken rock is a basic research topic among a series of key projects about stability control of the surrounding rocks in mines and the prevention of some disasters such as water inrush or gas outburst and the protection of the groundwater resource. It is of great theoretical and engineering importance in respect of promo- tion of security in mine production and sustainable development of the coal industry. According to the non-Darcy property of seepage flow in broken rock dynamic equations of non-Darcy and non-steady flows in broken rock are established. By dimensionless transformation, the solution diagram of steady-states satisfying the given boundary conditions is obtained. By numerical analysis of low relaxation iteration, the dynamic responses corresponding to the different flow parameters have been obtained. The stability analysis of the steady-states indicate that a saddle-node bifurcaton exists in the seepage flow system of broken rock. Consequently, using catastrophe theory, the fold catastrophe model of seepage flow instability has been obtained. As a result, the bifurcation curves of the seepage flow systems with different control parameters are presented and the standard potential function is also given with respect to the generalized state variable for the fold catastrophe of a dynamic system of seepage flow in broken rock.

Classification of parametrically constrained bifurcations

If the constraint boundary relates to a bifurcation parameter, a bifurcation is said to be parametrically constrained. Relying upon some substitution, a parametrically constrained bifurcation is transformed to an unconstrained bifurcation about new variables. A general form of transition sets of the parametrically constrained bifurcation is derived. The result indicates that only the constrained bifurcation set is influenced by parametric constraints, while other transition sets are the same as those of the corresponding nonparametrically constrained bifurcation. Taking parametrically constrained pitchfork bifurcation problems as examples, effects of parametric constraints on bifurcation classification are discussed.

Discrete Conley index and bifurcation points

In this paper, a sufficient condition for the existence of bifurcation points for discrete dynamical systems is presented. The relation between two families of systems is further discussed, and a sufficient condition for determining whether they may have the similar bifurcation points is given.

甲基转移酶SETDB1和SOX7甲基化在口腔癌中的相关性研究

目的检测口腔癌中SETDB1表达与SOX7甲基化水平,分析二者相关性及临床意义。方法收集口腔癌和癌旁组织,焦磷酸测序法检测SOX7基因甲基化水平,RT-qPCR检测SOX7和SETDB1 mRNA的表达,免疫组化及Western blot检测蛋白表达。统计分析SOX7甲基化水平与SETDB1相关性及其与临床病例特征的相关性。构建SETDB1下调siRNA转染口腔癌KB细胞,设siRNA-SETDB1为实验组(si-SET)、siRNA空载体为阴性对照组(si-N)和未转染KB细胞为空白对照组(NC)。检测3组SETDB1 mRNA和蛋白水平及SOX7甲基化。结果口腔癌组织SOX7基因甲基化率高于癌旁组织,SOX7 mRNA相对表达量低于癌旁组织,差异均有统计学意义(P<0.05)。癌组织中SETDB1 mRNA相对表达量高于癌旁组织(P<0.05);免疫组化结果显示癌组织SOX7蛋白表达阳性率SETDB1蛋白表达阳性率高于癌旁组织,差异均有统计学意义(P<0.05)。Western Blot结果显示SETDB1在癌组织中表达高于癌旁组织,SOX7在癌组织中表达低于癌旁组织,差异均有统计学意义(P<0.05);口腔癌组织中SOX7甲基化和SETDB1具有相关性(r=0.324,P<0.05);SOX7甲基化和SETDB1与肿瘤TNM分期、组织分化和淋巴结转移密切相关(P<0.05)。体外实验显示,RNA干扰SETDB1后si-RNA组中SETDB1 mRNA和蛋白表达量最低(P<0.05),SOX7基因甲基化率显著下降(P<0.05)。结论在口腔癌病变过程中SETDB1与SOX7基因甲基化具有相关性,SETDB1可能是催化SOX7发生甲基化修饰的重要甲基化转移酶,在口腔早期病变诊治中具潜在价值。

Singularly perturbed bifurcation subsystem and its application in power systems

The singularly perturbed bifurcation subsystem is described, and the test conditions of subsystem persistence are deduced. By use of fast and slow reduced subsystem model, the result does not require performing nonlinear transformation. Moreover, it is shown and proved that the persistence of the periodic orbits for Hopf bifurcation in the reduced model through center manifold. Van der Pol oscillator circuit is given to illustrate the persistence of bifurcation subsystems with the full dynamic system.

Characterization of static bifurcations for n-dimensional flows in the frequency domain

In this paper n-dimensional flows （described by continuous-time system） with static bifurcations are considered with the aim of classification of different elementary bifurcations using the frequency domain formalism. Based on frequency domain approach, we prove some criterions for the saddle-node bifurcation, transcritical bifurcation and pitchfork bifurcation, and give an example to illustrate the efficiency of the result obtained.

Local Stability Analysis and Bifurcations of a Discrete-Time Host-Parasitoid Model

In this paper, we examine a discrete-time Host-Parasitoid model which is a non-dimensionalized Nicholson and Bailey model. Phase portraits are drawn for different ranges of parameters and display the complicated dynamics of this system. We conduct the bifurcation analysis with respect to intrinsic growth rate r and searching efficiency a. Many forms of complex dynamics such as chaos, periodic windows are observed. Transition route to chaos dynamics is established via period-doubling bifurcations. Conditions of occurrence of the period-doubling, Neimark-Sacker and saddle-node bifurcations are analyzed for b≠a where a,b are searching efficiency. We study stable and unstable manifolds for different equilibrium points and coexistence of different attractors for this non-dimensionalize system. Without the parasitoid, the host population follows the dynamics of the Ricker model.

甲状腺乳头状癌组织中SETDB2、Gal-3、PLEKHS1的表达情况及其对患者预后的预测价值

目的分析SET结构域分叉组蛋白赖氨酸甲基转移酶2(SETDB2)、半乳糖凝集素3(Gal-3)、pleckstrin同源结构域S1(PLEKHS1)在甲状腺乳头状癌组织中的表达情况,以及三者对患者预后的预测价值。方法(1)选择118例甲状腺乳头状癌患者作为研究组,45例甲状腺良性结节患者作为对照组。采用免疫组化法检测甲状腺乳头状癌组织和甲状腺良性结节组织中SETDB2、Gal-3、PLEKHS1蛋白表达情况。比较研究组与对照组之间,以及不同特征甲状腺乳头状癌患者之间病灶组织中SETDB2、Gal-3、PLEKHS1蛋白的阳性表达率。(2)随访1年,记录甲状腺乳头状癌患者的生存情况。分析SETDB2、Gal-3、PLEKHS1蛋白阳性表达和阴性表达患者的生存率;比较预后良好和预后不良患者SETDB2、Gal-3、PLEKHS1蛋白的阳性表达率。采用受试者工作特征(ROC)曲线分析SETDB2、Gal-3、PLEKHS1对甲状腺乳头状癌患者预后的预测价值。结果(1)与对照组相比,研究组病灶组织中SETDB2蛋白阳性表达率较低,Gal-3、PLEKHS1蛋白阳性表达率较高(P<0.05)。在甲状腺乳头状癌患者中,Ⅲ~Ⅳ期、浸润深度≥1/2、组织中低分化、淋巴结转移、肿瘤直径>1 cm的患者病灶组织中SETDB2蛋白阳性表达率更低,Gal-3、PLEKHS1蛋白阳性表达率更高(P<0.05)。(2)在甲状腺乳头状癌患者中,SETDB2蛋白阳性表达患者生存率高于SETDB2蛋白阴性表达患者,Gal-3、PLEKHS1蛋白阳性表达患者生存率低于Gal-3、PLEKHS1蛋白阴性表达患者(P<0.05);预后良好患者的SETDB2蛋白阳性表达率高于预后不良患者,Gal-3、PLEKHS1蛋白阳性表达率低于预后不良患者(P<0.05)。ROC曲线分析结果显示,SETDB2、Gal-3、PLEKHS1蛋白总评分预测甲状腺乳头状癌患者预后不良的曲线下面积分别为0.826、0.841、0.859。结论在甲状腺乳头状癌中,SETDB2呈低表达,而Gal-3、PLEKHS1呈高表达,三者均与患者的病情严重程度相关,且对预后具有一定的预测价值。

Bifurcation analysis of an SIS epidemic model with a generalized non-monotonic and saturated incidence rate

In this paper,a new generalized non-monotonic and saturated incidence rate was introduced into a susceptible-infected-susceptible(SIS)epidemic model to account for inhibitory effect and crowding effect.The dynamic properties of the model were studied by qualitative theory and bifurcation theory.It is shown that when the infuence of psychological factors is large,the model has only disease-free equilibrium point,and this disease-free equilibrium point is globally asymptotically stable;when the influence of psychological factors is small,for some parameter conditions,the model has a unique endemic equilibrium point,which is a cusp point of co-dimension two,and for other parameter conditions the model has two endemic equilibrium points,one of which could be weak focus or center.In addition,the results of the model undergoing saddle-node bifurcation,Hopf bifurcation and Bogdanov-Takens bifurcation as the parameters vary were also proved.These results shed light on the impact of psychological behavior of susceptible people on the disease transmission.

Dynamic Analysis of an Algae-Bacteria Ecological Model

In the paper, under the framework of exploring the interaction between algae and bacteria, an algae-bacteria ecological model was established to analyze the interaction mechanism and growth coexistence mode between algicidal bacteria and algae. Firstly, mathematical work mainly provided some threshold conditions to ensure the occurrence of transcritical bifurcation and saddle-node bifurcation, which could provide certain theoretical support for selecting key ecological environmental factors and numerical simulations. Secondly, the numerical simulation work dynamically displayed the evolution process of the bifurcation dynamic behavior of the model (2.1) and the growth coexistence mode of algae and algicidal bacteria. Finally, it was worth summarizing that intrinsic growth rate and combined capture effort of algae population had a strong influence on the dynamic behavior of the model (2.1). Furthermore, it must also be noted that transcritical bifurcation and saddle-node bifurcation were the inherent driving forces behind the formation of steady-state growth coexistence mode between algicidal bacteria and algae. In summary, it was hoped that the results of this study would contribute to accelerating the study of the interaction mechanism between algicidal bacteria and algae.

结直肠癌中KRAS基因突变与SETDB1表达的相关性及临床意义

目的:探讨KRAS基因突变与SETDB1(set domain bifurcated 1)蛋白表达在结直肠癌中的临床意义及两者间的关系。方法:收集2017年1月至2017年12月于西南医科大学附属医院住院接受诊治的122例结直肠癌患者的组织标本及病例资料,采用二代测序技术(NGS)检测KRAS基因突变情况,免疫组织化学染色检测SETDB1蛋白的表达情况。结果:122例结直肠癌组织中KRAS基因突变率为41.8%,KRAS基因突变状态与肿瘤部位、术前血清CEA水平相关(P<0.05),与年龄、性别、分化程度、肿瘤大小、pT-NM分期、淋巴结转移等无关(P>0.05)。KRAS基因突变状态与SETDB1蛋白表达呈正相关(r=0.232,P=0.008)。SETDB1蛋白水平与肿瘤分化程度、大小及术前血清CEA水平相关(P<0.05),与年龄、性别、肿瘤部位、pTNM分期、淋巴结转移等无关(P>0.05)。结论:SETDB1蛋白在KRAS突变型结直肠癌组织中呈现高表达,KRAS基因突变可能影响SETDB1蛋白表达。

Bifurcation analysis and optimal control of an epidemic model with limited number of hospital beds

This paper deals with a three-dimensional nonlinear mathematical model to analyze an epidemic's future course when the public healthcare facilities,specifically the number of hospital beds,are limited.The feasibility and stability of the obtained equilibria are analyzed,and the basic reproduction number(Ro)is obtained.We show that the system exhibits transcritical bifurcation.To show the existence of Bogdanov-Takens bifurcation,we have derived the normal form.We have also discussed a generalized Hopf(or Bautin)bifurcation at which the first Lyapunov coefficient evanescences.To show the existence of saddle-node bifurcation,we used Sotomayor's theorem.Furthermore,we have identified an optimal layout of hospital beds in order to control the disease with minimum possible expenditure.An optimal control setting is studied analytically using optimal control theory,and numerical simulations of the optimal regimen are presented as well.

行星齿轮系扭转非线性振动建模与运动分岔特性研究

建立行星齿轮系扭转非线性振动模型,模型中考虑了行星齿轮系各齿轮副间的时变啮合刚度、齿侧间隙以及综合传递误差等非线性因素;推导出系统的量纲一振动微分方程,采用数值积分方法研究行星齿轮的运动特性随转速以及齿侧间隙等参数的分岔特性,结合Poincaré图形分析,研究转速、啮合阻尼以及齿侧间隙等参数对系统分岔特性的影响。结果发现,随着转速的逐渐增大,系统会通过激变途径进入到混沌运动,而随着齿侧间隙的逐渐增大,系统会通过倍周期分岔途径进入到混沌。阻尼过小将会导致行星齿轮系统的稳态运动由短周期运动向复杂运动转变。齿侧间隙是影响系统运动分岔特性的重要因素,但是影响范围主要限于量纲一齿侧间隙大于3.5的大间隙区段。

害虫种群动态模型的燕尾突变分析

在农田生态系统中,以作物状况、气象因素及天敌分别为3种控制变量,以害虫种群数量动态为状态变量,建立了燕尾突变模型,并用燕尾突变模型的性质分析害虫种群数量动态中产生的突变现象。具体对燕尾突变的分歧点集所分各个控制区域的系统势函数形式和平衡点情况进行了分析,说明了害虫种群数量发生突变的条件和机理,为实际应用提供理论依据。同时利用燕尾突变的性质直观描述了害虫种群数量变化中的突跳和滞后等现象。

水轮发电机组横向振动特性分析

推导建立了水轮发电机组系统动力学方程。对运动微分方程进行数值积分,分析了发电机转子的质量偏心及水轮机转子的质量偏心对水轮发电机组系统横向振动特性的影响。数值分析结果表明,发电机转子、水轮机转子的横向振动及大轴在上、下导轴承和水导轴承处的横向振动,经过充分衰减后,轴心轨迹都是圆形,但它们的半径并不相同。随着发电机转子的质量偏心的不断增加,大轴在3个导轴承处的横向振动出现了明显分岔现象,振动为周期1及复杂的拟周期运动。大轴在3个导轴承处的横向振动,随着水轮机转子的质量偏心的不断增大,没有出现分岔现象。

水轮发电机组转子不对中-碰摩耦合故障动力学分析

以水轮发电机组转子系统为研究对象，针对刚性联轴器综合不对中引起转子局部碰摩的问题，建立了机组转子不对中—碰摩耦合故障的动力学模型和微分方程，并利用数值积分方法研究该系统随不对中平行量和偏角参数变化的动力学行为。通过分岔图、Poincaré截面图、轴心轨迹图、时域波形图和幅值谱图系统地分析了发电机转子与水轮机转子在耦合故障下非线性动力学响应，发现机组转子系统随不对中平行量和偏角变化存在周期运动和复杂的拟周期，其碰摩过程非常复杂，机组故障特征频率除主要在1倍频外，还在0．3－0.4倍频处存在幅值较大的谐波分量。研究结果为水轮发电机组安全运行和准确识别转子不对中、碰摩故障提供有益的理论依据。