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Stochastic Bifurcation of an SIS Epidemic Model with Treatment and Immigration
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作者 Weipeng Zhang Dan Gu 《Journal of Applied Mathematics and Physics》 2024年第6期2254-2280,共27页
In this paper, we investigate an SIS model with treatment and immigration. Firstly, the two-dimensional model is simplified by using the stochastic averaging method. Then, we derive the local stability of the stochast... In this paper, we investigate an SIS model with treatment and immigration. Firstly, the two-dimensional model is simplified by using the stochastic averaging method. Then, we derive the local stability of the stochastic system by computing the Lyapunov exponent of the linearized system. Further, the global stability of the stochastic model is analyzed based on the singular boundary theory. Moreover, we prove that the model undergoes a Hopf bifurcation and a pitchfork bifurcation. Finally, several numerical examples are provided to illustrate the theoretical results. . 展开更多
关键词 Epidemic Model stochastic Averaging Method Singular Boundary Theory stochastic bifurcation
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Stochastic bifurcations of generalized Duffing–van der Pol system with fractional derivative under colored noise 被引量:6
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作者 李伟 张美婷 赵俊锋 《Chinese Physics B》 SCIE EI CAS CSCD 2017年第9期62-69,共8页
The stochastic bifurcation of a generalized Duffing–van der Pol system with fractional derivative under color noise excitation is studied. Firstly, fractional derivative in a form of generalized integral with time-de... The stochastic bifurcation of a generalized Duffing–van der Pol system with fractional derivative under color noise excitation is studied. Firstly, fractional derivative in a form of generalized integral with time-delay is approximated by a set of periodic functions. Based on this work, the stochastic averaging method is applied to obtain the FPK equation and the stationary probability density of the amplitude. After that, the critical parameter conditions of stochastic P-bifurcation are obtained based on the singularity theory. Different types of stationary probability densities of the amplitude are also obtained. The study finds that the change of noise intensity, fractional order, and correlation time will lead to the stochastic bifurcation. 展开更多
关键词 stochastic bifurcation fractional derivative color noise stochastic averaging method
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Analysis of stochastic bifurcation and chaos in stochastic Duffing-van der Pol system via Chebyshev polynomial approximation 被引量:5
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作者 马少娟 徐伟 +1 位作者 李伟 方同 《Chinese Physics B》 SCIE EI CAS CSCD 2006年第6期1231-1238,共8页
The Chebyshev polynomial approximation is applied to investigate the stochastic period-doubling bifurcation and chaos problems of a stochastic Duffing-van der Pol system with bounded random parameter of exponential pr... The Chebyshev polynomial approximation is applied to investigate the stochastic period-doubling bifurcation and chaos problems of a stochastic Duffing-van der Pol system with bounded random parameter of exponential probability density function subjected to a harmonic excitation. Firstly the stochastic system is reduced into its equivalent deterministic one, and then the responses of stochastic system can be obtained by numerical methods. Nonlinear dynamical behaviour related to stochastic period-doubling bifurcation and chaos in the stochastic system is explored. Numerical simulations show that similar to its counterpart in deterministic nonlinear system of stochastic period-doubling bifurcation and chaos may occur in the stochastic Duffing-van der Pol system even for weak intensity of random parameter. Simply increasing the intensity of the random parameter may result in the period-doubling bifurcation which is absent from the deterministic system. 展开更多
关键词 stochastic Duffing-van der Pol system Chebyshev polynomial approximation stochastic period-doubling bifurcation stochastic chaos
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Stochastic Bifurcation of Rectangular Thin Plate Vibration System Subjected to Axial Inplane Gaussian White Noise Excitation 被引量:1
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作者 葛根 王洪礼 许佳 《Transactions of Tianjin University》 EI CAS 2011年第1期13-19,共7页
A stochastic nonlinear dynamical model is proposed to describe the vibration of rectangular thin plate under axial inplane excitation considering the influence of random environment factors. Firstly, the model is simp... A stochastic nonlinear dynamical model is proposed to describe the vibration of rectangular thin plate under axial inplane excitation considering the influence of random environment factors. Firstly, the model is simplified by applying the stochastic averaging method of quasi-nonintegrable Hamilton system. Secondly, the methods of Lyapunov exponent and boundary classification associated with diffusion process are utilized to analyze the stochastic stability of the trivial solution of the system. Thirdly, the stochastic Hopf bifurcation of the vibration model is explored according to the qualitative changes in stationary probability density of system response, showing that the stochastic Hopf bifurcation occurs at two critical parametric values. Finally, some explanations are given in a simple way on the potential applications of stochastic stability and bifurcation analysis. 展开更多
关键词 rectangular thin plate stochastic stability stochastic Hopf bifurcation
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Stochastic bifurcation and density function analysis of a stochastic logistic equation with distributed delay and strong kernel
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作者 Xiaofeng Zhang Rong Yuan 《International Journal of Biomathematics》 SCIE 2023年第3期63-82,共20页
Since the stochastic bifurcation theory is still in its infancy,we try to analyze some stochastic bifurcation phenomenon from a simple mathematical model.Thus,this paper mainly focuses on studying the stochastic bifur... Since the stochastic bifurcation theory is still in its infancy,we try to analyze some stochastic bifurcation phenomenon from a simple mathematical model.Thus,this paper mainly focuses on studying the stochastic bifurcation of a stochastic logistic model with distributed delay in the strong kernel case,which is affected by noise.Therefore,we use the intrinsic growth rate as a bifurcation parameter.First,we study the stochastic D-bifurcation and stochastic P-bifurcation for stochastic logistic model.Furthermore,by deriving the corresponding Fokker-Planck equation,we obtain the expression of the joint density function of the stochastic logistic system near the positive equilibrium point.Finally,some conclusions are given. 展开更多
关键词 stochastic logistic model stochastic bifurcation density function Fokker-Planck equation
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Research on hunting stability and bifurcation characteristics of nonlinear stochastic wheelset system
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作者 Peng WANG Shaopu YANG +3 位作者 Yongqiang LIU Pengfei LIU Xing ZHANG Yiwei ZHAO 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2023年第3期431-446,共16页
A stochastic wheelset model with a nonlinear wheel-rail contact relationship is established to investigate the stochastic stability and stochastic bifurcation of the wheelset system with the consideration of the stoch... A stochastic wheelset model with a nonlinear wheel-rail contact relationship is established to investigate the stochastic stability and stochastic bifurcation of the wheelset system with the consideration of the stochastic parametric excitations of equivalent conicity and suspension stiffness.The wheelset is systematized into a onedimensional(1D)diffusion process by using the stochastic average method,the behavior of the singular boundary is analyzed to determine the hunting stability condition of the wheelset system,and the critical speed of stochastic bifurcation is obtained.The stationary probability density and joint probability density are derived theoretically.Based on the topological structure change of the probability density function,the stochastic Hopf bifurcation form and bifurcation condition of the wheelset system are determined.The effects of stochastic factors on the hunting stability and bifurcation characteristics are analyzed,and the simulation results verify the correctness of the theoretical analysis.The results reveal that the boundary behavior of the diffusion process determines the hunting stability of the stochastic wheelset system,and the left boundary characteristic value cL=1 is the critical state of hunting stability.Besides,stochastic D-bifurcation and P-bifurcation will appear in the wheelset system,and the critical speeds of the two kinds of stochastic bifurcation decrease with the increase in the stochastic parametric excitation intensity. 展开更多
关键词 stochastic wheelset system stochastic average method singular boundary hunting stability stochastic Hopf bifurcation
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Stochastic bifurcations in the SD (smooth and discontinuous) oscillator under bounded noise excitation 被引量:4
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作者 YUE XiaoLe XU Wei WANG Liang 《Science China(Physics,Mechanics & Astronomy)》 SCIE EI CAS 2013年第5期1010-1016,共7页
Stochastic bifurcations of the SD (smooth and discontinuous) oscillator with additive and/or multiplicative bounded noises are studied by the generalized cell mapping method using digraph analysis algorithm. From th... Stochastic bifurcations of the SD (smooth and discontinuous) oscillator with additive and/or multiplicative bounded noises are studied by the generalized cell mapping method using digraph analysis algorithm. From the global viewpoint, stochastic bifur- cation can be described as a sudden change in shape and size of a random attractor as the system parameter valies. The evolu- tionary process of stochastic bifurcation in the SD oscillator is shown in detail. Meanwhile, we show the phenomenon that un- der stochastic excitation the shape and size of random attractor and random saddle change along with the direction of unstable manifold. A plane stochastic bifurcation diagram is included. 展开更多
关键词 stochastic bifurcation SD oscillator generalized cell mapping method bounded noise
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Stochastic period-doubling bifurcation analysis of stochastic Bonhoeffer-van der Pol system 被引量:3
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作者 张莹 徐伟 +1 位作者 方同 徐旭林 《Chinese Physics B》 SCIE EI CAS CSCD 2007年第7期1923-1933,共11页
In this paper, the Chebyshev polynomial approximation is applied to the problem of stochastic period-doubling bifurcation of a stochastic Bonhoeffer-van der Pol (BVP for short) system with a bounded random parameter... In this paper, the Chebyshev polynomial approximation is applied to the problem of stochastic period-doubling bifurcation of a stochastic Bonhoeffer-van der Pol (BVP for short) system with a bounded random parameter. In the analysis, the stochastic BVP system is transformed by the Chebyshev polynomial approximation into an equivalent deterministic system, whose response can be readily obtained by conventional numerical methods. In this way we have explored plenty of stochastic period-doubling bifurcation phenomena of the stochastic BVP system. The numerical simulations show that the behaviour of the stochastic period-doubling bifurcation in the stochastic BVP system is by and large similar to that in the deterministic mean-parameter BVP system, but there are still some featured differences between them. For example, in the stochastic dynamic system the period-doubling bifurcation point diffuses into a critical interval and the location of the critical interval shifts with the variation of intensity of the random parameter. The obtained results show that Chebyshev polynomial approximation is an effective approach to dynamical problems in some typical nonlinear systems with a bounded random parameter of an arch-like probability density function. 展开更多
关键词 Chebyshev polynomial approximation stochastic Bonhoeffer-van der Pol system stochastic period-doubling bifurcation bounded random parameter
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STOCHASTIC HOPF BIFURCATION IN QUASIINTEGRABLE-HAMILTONIAN SYSTEMS 被引量:2
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作者 甘春标 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2004年第5期558-566,共9页
A new procedure is developed to study the stochastic Hopf bifurcation in quasi- integrable-Hamiltonian systems under the Gaussian white noise excitation.Firstly,the singular bound- aries of the first-class and their a... A new procedure is developed to study the stochastic Hopf bifurcation in quasi- integrable-Hamiltonian systems under the Gaussian white noise excitation.Firstly,the singular bound- aries of the first-class and their asymptotic stable conditions in probability are given for the averaged Ito differential equations about all the sub-system's energy levels with respect to the stochastic aver- aging method.Secondly,the stochastic Hopf bifurcation for the coupled sub-systems are discussed by defining a suitable bounded torus region in the space of the energy levels and employing the theory of the torus region when the singular boundaries turn into the unstable ones.Lastly,a quasi-integrable- Hamiltonian system with two degrees of freedom is studied in detail to illustrate the above procedure. Moreover,simulations by the Monte-Carlo method are performed for the illustrative example to verify the proposed procedure.It is shown that the attenuation motions and the stochastic Hopf bifurcation of two oscillators and the stochastic Hopf bifurcation of a single oscillator may occur in the system for some system's parameters.Therefore,one can see that the numerical results are consistent with the theoretical predictions. 展开更多
关键词 quasi-integrable-Hamiltonian system Gaussian white noise torus region stochastic Hopf bifurcation
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Stochastic period-doubling bifurcation in biharmonic driven Duffing system with random parameter
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作者 徐伟 马少娟 谢文贤 《Chinese Physics B》 SCIE EI CAS CSCD 2008年第3期857-864,共8页
Stochastic period-doubling bifurcation is explored in a forced Duffing system with a bounded random parameter as an additional weak harmonic perturbation added to the system. Firstly, the biharmonic driven Duffing sys... Stochastic period-doubling bifurcation is explored in a forced Duffing system with a bounded random parameter as an additional weak harmonic perturbation added to the system. Firstly, the biharmonic driven Duffing system with a random parameter is reduced to its equivalent deterministic one, and then the responses of the stochastic system can be obtained by available effective numerical methods. Finally, numerical simulations show that the phase of the additional weak harmonic perturbation has great influence on the stochastic period-doubling bifurcation in the biharmonic driven Duffing system. It is emphasized that, different from the deterministic biharmonic driven Duffing system, the intensity of random parameter in the Duffing system can also be taken as a bifurcation parameter, which can lead to the stochastic period-doubling bifurcations. 展开更多
关键词 random parameter stochastic Duffing system stochastic period-doubling bifurcation orthogonal polynomial approximation
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Stochastic period-doubling bifurcation analysis of a Rssler system with a bounded random parameter
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作者 倪菲 徐伟 +1 位作者 方同 岳晓乐 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第1期189-196,共8页
This paper aims to study the stochastic period-doubling bifurcation of the three-dimensional Rossler system with an arch-like bounded random parameter. First, we transform the stochastic RSssler system into its equiva... This paper aims to study the stochastic period-doubling bifurcation of the three-dimensional Rossler system with an arch-like bounded random parameter. First, we transform the stochastic RSssler system into its equivalent deterministic one in the sense of minimal residual error by the Chebyshev polynomial approximation method. Then, we explore the dynamical behaviour of the stochastic RSssler system through its equivalent deterministic system by numerical simulations. The numerical results show that some stochastic period-doubling bifurcation, akin to the conventional one in the deterministic case, may also appear in the stochastic Rossler system. In addition, we also examine the influence of the random parameter intensity on bifurcation phenomena in the stochastic Rossler system. 展开更多
关键词 Chebyshev polynomial approximation stochastic RSssler system stochastic period doubling bifurcation bounded random parameter
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NONLINEAR STOCHASTIC DYNAMICS: A SURVEY OF RECENT DEVELOPMENTS 被引量:19
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作者 朱位秋 蔡国强 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2002年第6期551-566,共16页
This paper provides an overview of significant advances in nonlinear stochastic dynamics during the past two decades, including random response, stochastic stability, stochastic bifurcation, first passage problem and ... This paper provides an overview of significant advances in nonlinear stochastic dynamics during the past two decades, including random response, stochastic stability, stochastic bifurcation, first passage problem and nonlinear stochastic control. Topics for future research are also suggested. 展开更多
关键词 nonlinear system random vibration stochastic stability stochastic bifurcation first passage problem
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Stochastic responses of Duffing–Van der Pol vibro-impact system under additive colored noise excitation 被引量:1
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作者 李超 徐伟 +1 位作者 王亮 李东喜 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第11期159-165,共7页
A response analysis procedure is developed for a vibro-impact system excited by colored noise. The non-smooth transformation is used to convert the vibro-impact system into a new system without impact term. With the h... A response analysis procedure is developed for a vibro-impact system excited by colored noise. The non-smooth transformation is used to convert the vibro-impact system into a new system without impact term. With the help of the modified quasi-conservative averaging, the total energy of the new system can be approximated as a Markov process, and the stationary probability density function (PDF) of the total energy is derived. The response PDFs of the original system are obtained using the analytical solution of the stationary PDF of the total energy. The validity of the theoretical results is tested through comparison with the corresponding simulation results. Moreover, stochastic bifurcations are also explored. 展开更多
关键词 vibro-impact system colored noise non-smooth transformation stochastic bifurcation
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ELEMENTARY BIFURCATIONS FOR A SIMPLE DYNAMICAL SYSTEM UNDER NON-GAUSSIAN LVY NOISES
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作者 陈慧琴 段金桥 张诚坚 《Acta Mathematica Scientia》 SCIE CSCD 2012年第4期1391-1398,共8页
Nonlinear dynamical systems are sometimes under the influence of random fluctuations. It is desirable to examine possible bifurcations for stochastic dynamical systems when a parameter varies.A computational analysis ... Nonlinear dynamical systems are sometimes under the influence of random fluctuations. It is desirable to examine possible bifurcations for stochastic dynamical systems when a parameter varies.A computational analysis is conducted to investigate bifurcations of a simple dynamical system under non-Gaussian a-stable Levy motions, by examining the changes in stationary probability density functions for the solution orbits of this stochastic system. The stationary probability density functions are obtained by solving a nonlocal Fokker-Planck equation numerically. This allows numerically investigating phenomenological bifurcation, or P-bifurcation, for stochastic differential equations with non-Gaussian Levy noises. 展开更多
关键词 stochastic dynamical systems non-Gaussian Levy motion Levy jump mea-sure stochastic bifurcation impact of non-Gaussian noises
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The Stochastic stability of a Logistic model with Poisson white noise
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作者 段东海 徐伟 +1 位作者 苏军 周丙常 《Chinese Physics B》 SCIE EI CAS CSCD 2011年第3期59-63,共5页
The stochastic stability of a logistic model subjected to the effect of a random natural environment, modeled as Poisson white noise process, is investigated. The properties of the stochastic response are discussed fo... The stochastic stability of a logistic model subjected to the effect of a random natural environment, modeled as Poisson white noise process, is investigated. The properties of the stochastic response are discussed for calculating the Lyapunov exponent, which had proven to be the most useful diagnostic tool for the stability of dynamical systems. The generalised Itp differentiation formula is used to analyse the stochastic stability of the response. The results indicate that the stability of the response is related to the intensity and amplitude distribution of the environment noise and the growth rate of the species. 展开更多
关键词 Poisson white noise Ito formula Lyapunov exponent stochastic bifurcation
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A stochastic epidemic model on homogeneous networks
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作者 刘茂省 阮炯 《Chinese Physics B》 SCIE EI CAS CSCD 2009年第12期5111-5116,共6页
In this paper, a stochastic SIS epidemic model on homogeneous networks is considered. The largest Lyapunov exponent is calculated by Oseledec multiplicative ergodic theory, and the stability condition is determined by... In this paper, a stochastic SIS epidemic model on homogeneous networks is considered. The largest Lyapunov exponent is calculated by Oseledec multiplicative ergodic theory, and the stability condition is determined by the largest Lyapunov exponent. The probability density function for the proportion of infected individuals is found explicitly, and the stochastic bifurcation is analysed by a probability density function. In particular, the new basic reproductive number R^*, that governs whether an epidemic with few initial infections can become an endemic or not, is determined by noise intensity. In the homogeneous networks, despite of the basic productive number R0 〉1, the epidemic will die out as long as noise intensity satisfies a certain condition. 展开更多
关键词 homogeneous networks SIS epidemic model stochastic stability stochastic bifurcation
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Bifurcation in most probable phase portraits for a bistable kinetic model with coupling Gaussian and non-Gaussian noises
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作者 Mengjiao HUA Yu WU 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2021年第12期1759-1770,共12页
The phenomenon of stochastic bifurcation driven by the correlated non-Gaussian colored noise and the Gaussian white noise is investigated by the qualitative changes of steady states with the most probable phase portra... The phenomenon of stochastic bifurcation driven by the correlated non-Gaussian colored noise and the Gaussian white noise is investigated by the qualitative changes of steady states with the most probable phase portraits.To arrive at the Markovian approximation of the original non-Markovian stochastic process and derive the general approximate Fokker-Planck equation(FPE),we deal with the non-Gaussian colored noise and then adopt the unified colored noise approximation(UCNA).Subsequently,the theoretical equation concerning the most probable steady states is obtained by the maximum of the stationary probability density function(SPDF).The parameter of the uncorrelated additive noise intensity does enter the governing equation as a non-Markovian effect,which is in contrast to that of the uncorrelated Gaussian white noise case,where the parameter is absent from the governing equation,i.e.,the most probable steady states are mainly controlled by the uncorrelated multiplicative noise.Additionally,in comparison with the deterministic counterpart,some peculiar bifurcation behaviors with regard to the most probable steady states induced by the correlation time of non-Gaussian colored noise,the noise intensity,and the non-Gaussian noise deviation parameter are discussed.Moreover,the symmetry of the stochastic bifurcation diagrams is destroyed when the correlation between noises is concerned.Furthermore,the feasibility and accuracy of the analytical predictions are verified compared with those of the Monte Carlo(MC)simulations of the original system. 展开更多
关键词 stochastic bifurcation non-Gaussian colored noise most probable steady state Fokker-Planck equation(FPE) Monte Carlo(MC)simulation
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Nonlinear dynamic characteristics and optimal control of a giant magnetostrictive film-shaped memory alloy composite plate subjected to in-plane stochastic excitation 被引量:2
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作者 竺致文 张庆昕 许佳 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第8期165-171,共7页
The nonlinear dynamic characteristics and optimal control of a giant magnetostrictive film (GMF)-shaped memory alloy (SMA) composite plate subjected to in-plane stochastic excitation are studied. GMF is prepared b... The nonlinear dynamic characteristics and optimal control of a giant magnetostrictive film (GMF)-shaped memory alloy (SMA) composite plate subjected to in-plane stochastic excitation are studied. GMF is prepared based on an SMA plate, and combined into a GMF-SMA composite plate. The Van der Pol item is improved to explain the hysteretic phenomena of GMF and SMA, and the nonlinear dynamics model of a GMF-SMA composite cantilever plate subjected to in-plane stochastic excitation is developed. The stochastic stability of the system is analyzed, and the steady-state probability density function of the dynamic response of the system is obtained. The condition of stochastic Hopf bifurcation is discussed, the reliability function of the system is provided, and then the probability density of the first-passage time is given. Finally, the stochastic optimal control strategy is proposed by the stochastic dynamic programming method. Numerical simulation shows that the stability of the trivial solution varies with bifurcation parameters, and stochastic Hopf bifurcation appears in the process; the system's reliability is improved through stochastic optimal control, and the first- passage time is delayed. A GMF-SMA composite plate combines the advantages of GMF and SMA, and can reduce vibration through passive control and active control effectively. The results are helpful for the engineering applications of GMF-SMA composite plates. 展开更多
关键词 giant magnetostrictive film shape memory alloy composite cantilever plate stochastic Hopf bifurcation optimal control
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Dynamic responses of an energy harvesting system based on piezoelectric and electromagnetic mechanisms under colored noise
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作者 杨勇歌 孟运 +1 位作者 曾远辉 孙亚辉 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第9期108-115,共8页
Because of the increasing demand for electrical energy,vibration energy harvesters(VEHs)that convert vibratory energy into electrical energy are a promising technology.In order to improve the efficiency of harvesting ... Because of the increasing demand for electrical energy,vibration energy harvesters(VEHs)that convert vibratory energy into electrical energy are a promising technology.In order to improve the efficiency of harvesting energy from environmental vibration,here we investigate a hybrid VEH.Unlike previous studies,this article analyzes the stochastic responses of the hybrid piezoelectric and electromagnetic energy harvesting system with viscoelastic material under narrow-band(colored)noise.Firstly,a mass-spring-damping system model coupled with piezoelectric and electromagnetic circuits under fundamental acceleration excitation is established,and analytical solutions to the dimensionless equations are derived.Then,the formula of the amplitude-frequency responses in the deterministic case and the first-order and secondorder steady-state moments of the amplitude in the stochastic case are obtained by using the multi-scales method.The amplitude-frequency analytical solutions are in good agreement with the numerical solutions obtained by the Monte Carlo method.Furthermore,the stochastic bifurcation diagram is plotted for the first-order steady-state moment of the amplitude with respect to the detuning frequency and viscoelastic parameter.Eventually,the influence of system parameters on mean-square electric voltage,mean-square electric current and mean output power is discussed.Results show that the electromechanical coupling coefficients,random excitation and viscoelastic parameter have a positive effect on the output power of the system. 展开更多
关键词 hybrid vibration energy harvesting narrow-band random excitation multi-scales method viscoelastic material stochastic bifurcation
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Bifurcation and Stability Analysis of Time-Delayed Wheelset System under White Noise Excitation
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作者 WANG Xinyang ZHANG Jiangang 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2024年第5期419-429,共11页
Considering the impact of time delay in the lateral stiffness of the primary suspension and stochastic disturbances of equivalent conicity on the wheelset system, a stochastic time-delayed wheelset system is establish... Considering the impact of time delay in the lateral stiffness of the primary suspension and stochastic disturbances of equivalent conicity on the wheelset system, a stochastic time-delayed wheelset system is established. The wheelset system is transformed into a onedimensional Ito stochastic differential equation using central manifold and stochastic averaging methods. The analysis of the system's stochastic stability is conducted through the maximum Lyapunov exponent and singular boundary theory. The combination of the stationary probability density method and numerical simulation is employed to discuss the types and conditions of stochastic P-bifurcation in the wheelset system. The results indicate that changes in speed and time delay induce stochastic P-bifurcations in the wheelset system, while changes in noise intensity do not lead to stochastic P-bifurcations. Both time delay and equivalent conicity affect the critical speed of the wheelset system, and the critical speed gradually increases with the decrease of time delay and equivalent conicity. 展开更多
关键词 wheelset system time delay central manifold stochastic stability stochastic bifurcation
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