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...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.展开更多
Seizures are caused by increased neuronal firing activity resulting from reduced inhibitory effect and enhancement of inhibitory modulation to suppress this activity is used as a therapeutic tool.However,recent experi...Seizures are caused by increased neuronal firing activity resulting from reduced inhibitory effect and enhancement of inhibitory modulation to suppress this activity is used as a therapeutic tool.However,recent experiments have shown a counterintuitive phenomenon that inhibitory modulation does not suppress but elicit post-inhibitory rebound(PIR)spike along with seizure to challenge the therapeutic tool.The nonlinear mechanism to avoid the PIR spike can present theoretical guidance to seizure treatment.This paper focuses on identifying credible bifurcations that underlie PIR spike by modulating multiple parameters in multiple theoretical models.The study identifies a codimension-2 bifurcation called saddle-node homoclinic orbit(SNHOB),which is an intersection between saddle node bifurcation on invariant cycle(SNIC)and other two bifurcations.PIR spike cannot be evoked for the SNIC far from the SNHOBbut induced for the SNIC close to the SNHOB,which extends the bifurcation condition for PIR spike from the well-known Hopf to SNIC.Especially,in a thalamic neuron model,increases of conductance of T-type Ca^(2+)(TC a)channel induce SNIC bifurcation approaching to the SNHOB to elicit PIR spikes,closely matching experimental results of the absence seizure or Parkinson diseases.Such results imply that,when inhibition is employed to relieve absence seizure and Parkinson diseases related to PIR spike,modulating SNIC to get far from the SNHOBto avoid PIR spike is the principle.The study also addresses the complex roles of TCacurrent and comprehensive relationships between PIR spike and nonlinear conceptions such as bifurcation types and shapes of threshold curve.展开更多
Dynamical behavior of nonlinear oscillator under combined parametric and forcing excitation, which includes yon der Pol damping, is very complex. In this paper, Melnikov's method is used to study the heteroclinic ...Dynamical behavior of nonlinear oscillator under combined parametric and forcing excitation, which includes yon der Pol damping, is very complex. In this paper, Melnikov's method is used to study the heteroclinic orbit bifurcations, subharmonic bifurcations and chaos in this system. Smale horseshoes and chaotic motions can occur from odd subharmonic bifurcation of infinite order in this system-far various resonant cases finally the numerical computing method is used to study chaotic motions of this system. The results achieved reveal some new phenomena.展开更多
We investigate an important relationship that exists between the Hopf bifurcation in the singularly perturbed nonlinear power systems and the singularity induced bifurcations (SIBs) in the corresponding different- tia...We investigate an important relationship that exists between the Hopf bifurcation in the singularly perturbed nonlinear power systems and the singularity induced bifurcations (SIBs) in the corresponding different- tial-algebraic equations (DAEs). In a generic case, the SIB phenomenon in a system of DAEs signals Hopf bifurcation in the singularly perturbed systems of ODEs. The analysis is based on the linear matrix pencil theory and polynomials with parameter dependent coefficients. A few numerical examples are included.展开更多
Linear transfer function approximations of the fractional integrators 1Is~ with m ^- 0.80-0.99 with steps of 0.01 are calculated systemically from the fractional order calculus and frequency-domain approximation metho...Linear transfer function approximations of the fractional integrators 1Is~ with m ^- 0.80-0.99 with steps of 0.01 are calculated systemically from the fractional order calculus and frequency-domain approximation method. To illustrate the effectiveness for fractional functions, the magnitude Bode diagrams of the actual and approximate transfer functions 1Ism with a slope of -20m dB//decade are depicted. By using the transfer function approxima- tions of the fractional integrators, a new fractional-order nonlinear system is investigated through the bifurcation diagram and Lyapunov exponent. The corresponding circuit of the fractional-order system is designed and the experimental results match perfectly with the numerical simulations.展开更多
Biforations of an ordinary differential equation with two-point boundary value condition are investigated. Using the singularity theory based on the Liapunov-Schmidt reduction, we have obtained some characterization r...Biforations of an ordinary differential equation with two-point boundary value condition are investigated. Using the singularity theory based on the Liapunov-Schmidt reduction, we have obtained some characterization results.展开更多
The stability of a heat-conducting flow due to the pumping of a fluid around the annulus of horizontal porous cylinders is studied. The basic flow is under the action of radial flow and a radial temperature gradient. ...The stability of a heat-conducting flow due to the pumping of a fluid around the annulus of horizontal porous cylinders is studied. The basic flow is under the action of radial flow and a radial temperature gradient. The objects of investigations are different regimes and bifurcations which may arise in this flow.展开更多
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 dynam...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 <em>r</em> and searching efficiency <em>a</em>. 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 <em>b≠a</em> where <em>a,b</em> 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.展开更多
This paper studies interactions of pipe and fluid and deals with bifurcations of a cantilevered pipe conveying a steady fluid, clamped at one end and having a nozzle subjected to nonlinear constraints at the free end....This paper studies interactions of pipe and fluid and deals with bifurcations of a cantilevered pipe conveying a steady fluid, clamped at one end and having a nozzle subjected to nonlinear constraints at the free end. Either the nozzle parameter or the flow velocity is taken as a variable parameter. The discrete equations of the system are obtained by the Ritz-Galerkin method. The static stability is studied by the Routh criteria. The method of averaging is employed to investigate the stability of the periodic motions. A Runge-Kutta scheme is used to examine the analytical results and the chaotic motions. Three critical values are given. The first one makes the system lose the static stability by pitchfork bifurcation. The second one makes the system lose the dynamical stability by Hopf bifurcation. The third one makes the periodic motions of the system lose the stability by doubling-period bifurcation.展开更多
In this paper, we investigate a low dimensional model of percussive drilling with vibro-impact to mimic the nonlinear dynamics of the bounded progression. Non- holonomity which arises in the stick-slip caused by the i...In this paper, we investigate a low dimensional model of percussive drilling with vibro-impact to mimic the nonlinear dynamics of the bounded progression. Non- holonomity which arises in the stick-slip caused by the impact during drilling fails to be correctly identified via the classical techniques. A reduced model without non-holono- mity is derived by the introduction of a new state variable, of which averaging technique is employed successfully to detect the periodic motions. Local bifurcations are presented directly by using C-L method. Numerical simulations and the penetrating rate analysis along different choices of parame- ters have been carried out to probe the nonlinear behaviour and the optimal penetrating rate of the drilling system.展开更多
The bifurcations of penetrative Rayleigh-B′enard convection in cylindrical containers are studied by the linear stability analysis(LSA) combined with the direct numerical simulation(DNS) method. The working ?uid is c...The bifurcations of penetrative Rayleigh-B′enard convection in cylindrical containers are studied by the linear stability analysis(LSA) combined with the direct numerical simulation(DNS) method. The working ?uid is cold water near 4?C, where the Prandtl number P r is 11.57, and the aspect ratio(radius/height) of the cylinder ranges from 0.66 to 2. It is found that the critical Rayleigh number increases with the increase in the density inversion parameter θ_m. The relationship between the normalized critical Rayleigh number(Rac(θ_m)/Rac(0)) and θ_m is formulated, which is in good agreement with the stability results within a large range of θ_m. The aspect ratio has a minor effect on Rac(θ_m)/Rac(0). The bifurcation processes based on the axisymmetric solutions are also investigated. The results show that the onset of axisymmetric convection occurs through a trans-critical bifurcation due to the top-bottom symmetry breaking of the present system.Moreover, two kinds of qualitatively different steady axisymmetric solutions are identi?ed.展开更多
We propose an impulsive hybrid control method to control the period-doubling bifurcations and stabilize unstable periodic orbits embedded in a chaotic attractor of a small-world network. Simulation results show that t...We propose an impulsive hybrid control method to control the period-doubling bifurcations and stabilize unstable periodic orbits embedded in a chaotic attractor of a small-world network. Simulation results show that the bifurcations can be delayed or completely eliminated. A periodic orbit of the system can be controlled to any desired periodic orbit by using this method.展开更多
The nonlinear behavior of a cantilevered fluid conveying pipe subjected to principal parametric and internal resonances is investigated in this paper.The flow velocity is divided into constant and sinusoidal parts.The...The nonlinear behavior of a cantilevered fluid conveying pipe subjected to principal parametric and internal resonances is investigated in this paper.The flow velocity is divided into constant and sinusoidal parts.The velocity value of the constant part is so adjusted such that the system exhibits 3:1 internal resonances for the first two modes.The method of multiple scales is employed to obtain the response of the system and a set of four first-order nonlinear ordinary- differential equations for governing the amplitude of the response.The eigenvalues of the Jacobian matrix are used to assess the stability of the equilibrium solutions with varying parameters.The co- dimension 2 derived from the double-zero eigenvalues is analyzed in detail.The results show that the response amplitude may undergo saddle-node,pitchfork,Hopf,homoclinic loop and period- doubling bifurcations depending on the frequency and amplitude of the sinusoidal flow.When the frequency of the sinusoidal flow equals exactly half of the first-mode frequency,the system has a route to chaos by period-doubling bifurcation and then returns to a periodic motion as the amplitude of the sinusoidal flow increases.展开更多
The effects of the supported angle on the stability and dynamical bifurcations of an inclined cantilevered pipe conveying fluid are investigated. First, a theoretical model of the pipe is developed through the force b...The effects of the supported angle on the stability and dynamical bifurcations of an inclined cantilevered pipe conveying fluid are investigated. First, a theoretical model of the pipe is developed through the force balance and stress-strain relationship. Second, the response surfaces, stability, and critical lines of the typical hanging system (H-S) and standing system (S-S) are discussed based on the modal analysis. Last, the bifurcation diagrams of the pipe are presented for different supported angles. It is shown that pipes will undergo a series of bifurcation processes and show rich dynamic phenomena such as buckling, Hopf bifurcation, period-doubling bifurcation, chaotic motion, and divergence motion.展开更多
An impulsive delayed feedback control strategy to control period-doubling bifurcations and chaos is proposed. The control method is then applied to a discrete small-world network model. Qualitative analyses and simula...An impulsive delayed feedback control strategy to control period-doubling bifurcations and chaos is proposed. The control method is then applied to a discrete small-world network model. Qualitative analyses and simulations show that under a generic condition, the bifurcations and the chaos can be delayed or eliminated completely. In addition, the periodic orbits embedded in the chaotic attractor can be stabilized.展开更多
A computational simulation for the separation of red blood cells (RBCs) is presented.The deformability of RBCs is expressed by the spring network model,which is based on the minimum energy principle.In the computation...A computational simulation for the separation of red blood cells (RBCs) is presented.The deformability of RBCs is expressed by the spring network model,which is based on the minimum energy principle.In the computation of the fluid flow,the lattice Boltzmann method is used to solve the Navier-Stokes equations.Coupling of the fluid-membrane interaction is carried out by using the immersed boundary method.To verify our method,the motions of RBCs in shear flow are simulated.Typical motions of RBCs observed in the experiments are reproduced,including tank-treading,swinging and tumbling.The motions of 8 RBCs at the bifurcation are simulated when the two daughter vessels have different ratios.The results indicate that when the ratio of the daughter vessel diameter becomes smaller,the distribution of RBCs in the two vessels becomes more non-uniform.展开更多
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
Objective To describe changes that occur in stent morphology and structure after its implantation in coronary bifurcation.Side branch (SB) compromise after stenting of main vessel in coronary bifurcation is a major in...Objective To describe changes that occur in stent morphology and structure after its implantation in coronary bifurcation.Side branch (SB) compromise after stenting of main vessel in coronary bifurcation is a major intraprocedural problem and for the long term,as a place of restenosis.Methods We created an elastic wall model (parent vessel diameter 3.5mm,daughter branches 3.5mm and 2.75mm)with 30,45 and 60 degree distal angulation between branches.After stent implantation,struts to the side branch were opened with 2.0mm and consequently 3.0mm diameter balloons.Subsequent balloon redilatations and kissing balloon inflations (KBI) were performed.All stages of the procedure were photographed with magnification up to 100 times.Results We found that the leading mechanism for side branch compromise was carina displacement,and discovered theoretical description for expected ostial stenosis severity.Based on our model we found that displacement of bifurcation flow divider cause SB stenosis with almost perfect coincidence with our theoretical predictions.Opening of stent cells through the proximal and distal stent struts always increased interslrut distance,but never achieved good apposition to the wall.Balloon diameter increase didn't give proportional enlargement in stent cell diameters.KBI leads to some small better stent positioning,correcting main vessel strut dislodgment from wall,but never gave full strut-wall contact.Distance between struts and wall was minimal only when the stent cell perfectly faced ostium of SB.This was also our observation that the shape of ostium of SB becomed eUiptically-bean shaped after stent implantation and generally kept that shape during consequent stages of experiment.Measured diameter and area stenosis were perfectly fitted and theoretically predicted from our concept Conclusion We have described stent-wall deformations in stent-balloon technique for treatment of coronary bifurcation demonstrating carina displacement as possibly main mechanism of side branch compromise after main vessel stenting.We have shown that KBI could not give full strut-wall contact if there is no perfect facing of stem cell and SB ostium.(J Geroatr Cardool 2008;5(1):43-49)展开更多
基金financial support from K.N.Toosi University of Technology,Tehran,Iran。
文摘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.
基金the National Natural Science Foundation of China(Grant Nos.12072236,11872276,and11802086)the Postdoctoral Research Project of Henan Province,China(Grant No.19030095)the Science and Technology Development Program of Henan Province,China(Grant No.212102210543)。
文摘Seizures are caused by increased neuronal firing activity resulting from reduced inhibitory effect and enhancement of inhibitory modulation to suppress this activity is used as a therapeutic tool.However,recent experiments have shown a counterintuitive phenomenon that inhibitory modulation does not suppress but elicit post-inhibitory rebound(PIR)spike along with seizure to challenge the therapeutic tool.The nonlinear mechanism to avoid the PIR spike can present theoretical guidance to seizure treatment.This paper focuses on identifying credible bifurcations that underlie PIR spike by modulating multiple parameters in multiple theoretical models.The study identifies a codimension-2 bifurcation called saddle-node homoclinic orbit(SNHOB),which is an intersection between saddle node bifurcation on invariant cycle(SNIC)and other two bifurcations.PIR spike cannot be evoked for the SNIC far from the SNHOBbut induced for the SNIC close to the SNHOB,which extends the bifurcation condition for PIR spike from the well-known Hopf to SNIC.Especially,in a thalamic neuron model,increases of conductance of T-type Ca^(2+)(TC a)channel induce SNIC bifurcation approaching to the SNHOB to elicit PIR spikes,closely matching experimental results of the absence seizure or Parkinson diseases.Such results imply that,when inhibition is employed to relieve absence seizure and Parkinson diseases related to PIR spike,modulating SNIC to get far from the SNHOBto avoid PIR spike is the principle.The study also addresses the complex roles of TCacurrent and comprehensive relationships between PIR spike and nonlinear conceptions such as bifurcation types and shapes of threshold curve.
文摘Dynamical behavior of nonlinear oscillator under combined parametric and forcing excitation, which includes yon der Pol damping, is very complex. In this paper, Melnikov's method is used to study the heteroclinic orbit bifurcations, subharmonic bifurcations and chaos in this system. Smale horseshoes and chaotic motions can occur from odd subharmonic bifurcation of infinite order in this system-far various resonant cases finally the numerical computing method is used to study chaotic motions of this system. The results achieved reveal some new phenomena.
文摘We investigate an important relationship that exists between the Hopf bifurcation in the singularly perturbed nonlinear power systems and the singularity induced bifurcations (SIBs) in the corresponding different- tial-algebraic equations (DAEs). In a generic case, the SIB phenomenon in a system of DAEs signals Hopf bifurcation in the singularly perturbed systems of ODEs. The analysis is based on the linear matrix pencil theory and polynomials with parameter dependent coefficients. A few numerical examples are included.
基金Supported by the National Natural Science Foundation of China under Grant No 51475246the Natural Science Foundation of Jiangsu Province under Grant No Bk20131402the Ministry-of-Education Overseas Returnees Start-up Research Fund under Grant No[2012]1707
文摘Linear transfer function approximations of the fractional integrators 1Is~ with m ^- 0.80-0.99 with steps of 0.01 are calculated systemically from the fractional order calculus and frequency-domain approximation method. To illustrate the effectiveness for fractional functions, the magnitude Bode diagrams of the actual and approximate transfer functions 1Ism with a slope of -20m dB//decade are depicted. By using the transfer function approxima- tions of the fractional integrators, a new fractional-order nonlinear system is investigated through the bifurcation diagram and Lyapunov exponent. The corresponding circuit of the fractional-order system is designed and the experimental results match perfectly with the numerical simulations.
基金the National Natural Science Foundation of China(19971057) and the Youth Science Foundation of ShanghaiMunicipal Commission
文摘Biforations of an ordinary differential equation with two-point boundary value condition are investigated. Using the singularity theory based on the Liapunov-Schmidt reduction, we have obtained some characterization results.
文摘The stability of a heat-conducting flow due to the pumping of a fluid around the annulus of horizontal porous cylinders is studied. The basic flow is under the action of radial flow and a radial temperature gradient. The objects of investigations are different regimes and bifurcations which may arise in this flow.
文摘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 <em>r</em> and searching efficiency <em>a</em>. 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 <em>b≠a</em> where <em>a,b</em> 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.
基金The project supported by the Science Foundation of Tongji UniversityNational Key Projects of China under Grant No.PD9521907
文摘This paper studies interactions of pipe and fluid and deals with bifurcations of a cantilevered pipe conveying a steady fluid, clamped at one end and having a nozzle subjected to nonlinear constraints at the free end. Either the nozzle parameter or the flow velocity is taken as a variable parameter. The discrete equations of the system are obtained by the Ritz-Galerkin method. The static stability is studied by the Routh criteria. The method of averaging is employed to investigate the stability of the periodic motions. A Runge-Kutta scheme is used to examine the analytical results and the chaotic motions. Three critical values are given. The first one makes the system lose the static stability by pitchfork bifurcation. The second one makes the system lose the dynamical stability by Hopf bifurcation. The third one makes the periodic motions of the system lose the stability by doubling-period bifurcation.
基金supported by the National Natural Science Foundation of China(10872136 and 10932006)the EPSRC Grant (GR/R85556)
文摘In this paper, we investigate a low dimensional model of percussive drilling with vibro-impact to mimic the nonlinear dynamics of the bounded progression. Non- holonomity which arises in the stick-slip caused by the impact during drilling fails to be correctly identified via the classical techniques. A reduced model without non-holono- mity is derived by the introduction of a new state variable, of which averaging technique is employed successfully to detect the periodic motions. Local bifurcations are presented directly by using C-L method. Numerical simulations and the penetrating rate analysis along different choices of parame- ters have been carried out to probe the nonlinear behaviour and the optimal penetrating rate of the drilling system.
基金Project supported by the National Natural Science Foundation of China(Nos.11572314,11621202,and 11772323)the Fundamental Research Funds for the Central Universities
文摘The bifurcations of penetrative Rayleigh-B′enard convection in cylindrical containers are studied by the linear stability analysis(LSA) combined with the direct numerical simulation(DNS) method. The working ?uid is cold water near 4?C, where the Prandtl number P r is 11.57, and the aspect ratio(radius/height) of the cylinder ranges from 0.66 to 2. It is found that the critical Rayleigh number increases with the increase in the density inversion parameter θ_m. The relationship between the normalized critical Rayleigh number(Rac(θ_m)/Rac(0)) and θ_m is formulated, which is in good agreement with the stability results within a large range of θ_m. The aspect ratio has a minor effect on Rac(θ_m)/Rac(0). The bifurcation processes based on the axisymmetric solutions are also investigated. The results show that the onset of axisymmetric convection occurs through a trans-critical bifurcation due to the top-bottom symmetry breaking of the present system.Moreover, two kinds of qualitatively different steady axisymmetric solutions are identi?ed.
基金supported by the Research Foundation for Outstanding Young Teachers of China University of Geosciences, China (Grant No CUGNL0637)the National Natural Science Foundation of China (Grant Nos 60573005, 60603006 and 60628301)
文摘We propose an impulsive hybrid control method to control the period-doubling bifurcations and stabilize unstable periodic orbits embedded in a chaotic attractor of a small-world network. Simulation results show that the bifurcations can be delayed or completely eliminated. A periodic orbit of the system can be controlled to any desired periodic orbit by using this method.
基金Project supported by the National Natural Science Foundation of China(No.10072039)RGC in City University of Hong Kong(No.7001206 and No.7001338).
文摘The nonlinear behavior of a cantilevered fluid conveying pipe subjected to principal parametric and internal resonances is investigated in this paper.The flow velocity is divided into constant and sinusoidal parts.The velocity value of the constant part is so adjusted such that the system exhibits 3:1 internal resonances for the first two modes.The method of multiple scales is employed to obtain the response of the system and a set of four first-order nonlinear ordinary- differential equations for governing the amplitude of the response.The eigenvalues of the Jacobian matrix are used to assess the stability of the equilibrium solutions with varying parameters.The co- dimension 2 derived from the double-zero eigenvalues is analyzed in detail.The results show that the response amplitude may undergo saddle-node,pitchfork,Hopf,homoclinic loop and period- doubling bifurcations depending on the frequency and amplitude of the sinusoidal flow.When the frequency of the sinusoidal flow equals exactly half of the first-mode frequency,the system has a route to chaos by period-doubling bifurcation and then returns to a periodic motion as the amplitude of the sinusoidal flow increases.
基金Project supported by the Science Fund for Creative Research Groups of the National Natural Science Foundation of China(No.51221004)the National Natural Science Foundation of China(Nos.11172260,11072213,and 51375434)the Higher School Specialized Research Fund for the Doctoral Program(No.20110101110016)
文摘The effects of the supported angle on the stability and dynamical bifurcations of an inclined cantilevered pipe conveying fluid are investigated. First, a theoretical model of the pipe is developed through the force balance and stress-strain relationship. Second, the response surfaces, stability, and critical lines of the typical hanging system (H-S) and standing system (S-S) are discussed based on the modal analysis. Last, the bifurcation diagrams of the pipe are presented for different supported angles. It is shown that pipes will undergo a series of bifurcation processes and show rich dynamic phenomena such as buckling, Hopf bifurcation, period-doubling bifurcation, chaotic motion, and divergence motion.
基金Project supported by the National Natural Science Foundation of China(Grant No.60974004)the Science Foundation of Ministry of Housing and Urban-Rural Development,China(Grant No.2011-K5-31)
文摘An impulsive delayed feedback control strategy to control period-doubling bifurcations and chaos is proposed. The control method is then applied to a discrete small-world network model. Qualitative analyses and simulations show that under a generic condition, the bifurcations and the chaos can be delayed or eliminated completely. In addition, the periodic orbits embedded in the chaotic attractor can be stabilized.
基金Partially supported by the Anhui Provincial Natural Science Foundation under Grant No 11040606M09.
文摘A computational simulation for the separation of red blood cells (RBCs) is presented.The deformability of RBCs is expressed by the spring network model,which is based on the minimum energy principle.In the computation of the fluid flow,the lattice Boltzmann method is used to solve the Navier-Stokes equations.Coupling of the fluid-membrane interaction is carried out by using the immersed boundary method.To verify our method,the motions of RBCs in shear flow are simulated.Typical motions of RBCs observed in the experiments are reproduced,including tank-treading,swinging and tumbling.The motions of 8 RBCs at the bifurcation are simulated when the two daughter vessels have different ratios.The results indicate that when the ratio of the daughter vessel diameter becomes smaller,the distribution of RBCs in the two vessels becomes more non-uniform.
基金Project supported by the National Natural Science Foundation of China(Grant No.11302157)the Natural Science Basic Research Plan in Shaanxi Province of China(Grant No.2015JM1028)+1 种基金the Fundamental Research Funds for the Central Universities,China(Grant No.JB160706)Chinese–Serbian Science and Technology Cooperation for the Years 2015-2016(Grant No.3-19)
文摘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.
文摘Objective To describe changes that occur in stent morphology and structure after its implantation in coronary bifurcation.Side branch (SB) compromise after stenting of main vessel in coronary bifurcation is a major intraprocedural problem and for the long term,as a place of restenosis.Methods We created an elastic wall model (parent vessel diameter 3.5mm,daughter branches 3.5mm and 2.75mm)with 30,45 and 60 degree distal angulation between branches.After stent implantation,struts to the side branch were opened with 2.0mm and consequently 3.0mm diameter balloons.Subsequent balloon redilatations and kissing balloon inflations (KBI) were performed.All stages of the procedure were photographed with magnification up to 100 times.Results We found that the leading mechanism for side branch compromise was carina displacement,and discovered theoretical description for expected ostial stenosis severity.Based on our model we found that displacement of bifurcation flow divider cause SB stenosis with almost perfect coincidence with our theoretical predictions.Opening of stent cells through the proximal and distal stent struts always increased interslrut distance,but never achieved good apposition to the wall.Balloon diameter increase didn't give proportional enlargement in stent cell diameters.KBI leads to some small better stent positioning,correcting main vessel strut dislodgment from wall,but never gave full strut-wall contact.Distance between struts and wall was minimal only when the stent cell perfectly faced ostium of SB.This was also our observation that the shape of ostium of SB becomed eUiptically-bean shaped after stent implantation and generally kept that shape during consequent stages of experiment.Measured diameter and area stenosis were perfectly fitted and theoretically predicted from our concept Conclusion We have described stent-wall deformations in stent-balloon technique for treatment of coronary bifurcation demonstrating carina displacement as possibly main mechanism of side branch compromise after main vessel stenting.We have shown that KBI could not give full strut-wall contact if there is no perfect facing of stem cell and SB ostium.(J Geroatr Cardool 2008;5(1):43-49)