In this paper we investigate the scalar field evolution in the dyadosphere spacetime by using the third-order WKB approximation. We find that the coupling term between the gravitation and the nonlinear electrodynamics...In this paper we investigate the scalar field evolution in the dyadosphere spacetime by using the third-order WKB approximation. We find that the coupling term between the gravitation and the nonlinear electrodynamics makes the scalar field decay more quickly and it also makes the scalar field oscillate more slowly. On the o'ther words, this coupling term takes effect on the scalar field evolution as a damping factor. At the same time these effects become more obvious for the scalar field with higher angle quantum number.展开更多
This paper describes the dynamic characteristics of pipelines laid through alluvial valleys. We assume that the alluvial valley has a semi-cylindrical cross-section. The ground motion of alluvial valley under harmonic...This paper describes the dynamic characteristics of pipelines laid through alluvial valleys. We assume that the alluvial valley has a semi-cylindrical cross-section. The ground motion of alluvial valley under harmonic seismic SH waves is carried out, and the pipeline-soil dynamic interaction is taken into account. Though simple, the model may qualitatively explain the earthquake damages of pipelines laid through an alluvial river valley.展开更多
Nonlinear interactions among incident wave, tank-sloshing and floating body coupling motion are investigated. The fully nonlinear sloshing and body-surface nonlinear free surface hydrodynamics is simulated using a Non...Nonlinear interactions among incident wave, tank-sloshing and floating body coupling motion are investigated. The fully nonlinear sloshing and body-surface nonlinear free surface hydrodynamics is simulated using a Non-Uniform Rational B-Spline (NURBS) higher-order panel method in time domain based on the potential theory. A robust and stable improved iterative procedure (Yan and Ma, 2007) for floating bodies is used for calculating the time derivative of velocity potential and floating body motion. An energy dissipation condition based on linear theory adopted by Huang (2011) is developed to consider flow viscosity effects of sloshing flow in nonlinear model. A two-dimensional tank model test was performed to identify its validity. The present nonlinear coupling sway motion results are subsequently compared with the corresponding Rognebakke and Faltinsen (2003)'s experimental results, showing fair agreement. Thus, the numerical approach presented in this paper is expected to be very efficient and realistic in evaluating the coupling effects of nonlinear sloshing and body motion.展开更多
Aiming at the problem of relative navigation for non-cooperative rendezvous of spacecraft,this paper proposes a new angles-only navigation architecture using non-linear dynamics method. This method does not solve the ...Aiming at the problem of relative navigation for non-cooperative rendezvous of spacecraft,this paper proposes a new angles-only navigation architecture using non-linear dynamics method. This method does not solve the problem of poor observability of angles-only navigation through orbital or attitude maneuvering,but improves the observability of angles-only navigation through capturing the non-linearity of the system in the evolution of relative motion. First,three relative dynamics models and their corresponding line-of-sight(LoS)measurement equations are introduced,including the rectilinear state relative dynamics model,the curvilinear state relative dynamics model,and the relative orbital elements(ROE)state relative dynamics model. Then,an observability analysis theory based on the Gramian matrix is introduced to determine which relative dynamics model could maximize the observability of angles-only navigation. Next,an adaptive extended Kalman filtering scheme is proposed to solve the problem that the angles-only navigation filter using the non-linear dynamics method is sensitive to measurement noises. Finally,the performances of the proposed angles-only navigation architecture are tested by means of numerical simulations,which demonstrates that the angles-only navigation filtering scheme without orbital or attitude maneuvering is completely feasible through improving the modeling of the relative dynamics and LoS measurement equations.展开更多
Automatic line reclosing schemes used in an extra-high-voltage power system is an economical and effective means to maintain transient stability. A novel method is proposed in the paper to adaptively optimize the auto...Automatic line reclosing schemes used in an extra-high-voltage power system is an economical and effective means to maintain transient stability. A novel method is proposed in the paper to adaptively optimize the automatic line reclosing time after a transient fault for enhancement of interconnected power system transient stability. Both the study on the transient energy over network and the structure-preserving multi-machines power system model illustrate that the excessive convergence of potential energy on the lines with a certain cutset deteriorate power system stability, and therefore, an optimum line reclosing strategy can be established by minimizing the change in transient potential energy distribution across a cutset lines in the vicinity of the faulty line as an optimization target, and the optimal reclosure time is set to the time of minimum line phase angle difference. Without any pre-determined knowledge, the method is adaptive to various power system operation modes and fault conditions, and easy to implement because only a limited number of data measured at one location on a tie-line linking sub-networks are required. Simulations have been performed with the OMIB(One Machine and Infinite Bus System) and a real inter-connected power system to verify the applicability of the method proposed.展开更多
We have set up a new reduced model Hamiltonian for the polariton system, in which the nonlinear interaction contains the rotating term k l ( a + b + ab+) and the attractive two-mode squeezed coupling - k2 ( a ...We have set up a new reduced model Hamiltonian for the polariton system, in which the nonlinear interaction contains the rotating term k l ( a + b + ab+) and the attractive two-mode squeezed coupling - k2 ( a + b+ + ab ) . The dynamical evolution of this system has been solved and the nonclassical features relevant to the second-order and high-order squeezing have been obtained in an analytical form. For the first time, in contrast to the existing result, we have confirmed for the phonon field that the attractive two-mode squeezed interaction will not only result in the second-order and high-order squeezing in X-component with the time evolution, but also in time average. Furthermore, the phenomena of collapse and revival of inversion will occur as well in the time evolution of the average number of photon and phonon, as also in the second-order and high-order squeezing of photon field, particularly, in the high-order squeezing of phonon field.展开更多
We investigate the statistical mechanics properties of a nonlinear dynamics model of the denaturation of the DNA double-helix and study the effects of salt concentration and temperature on denaturation transition of D...We investigate the statistical mechanics properties of a nonlinear dynamics model of the denaturation of the DNA double-helix and study the effects of salt concentration and temperature on denaturation transition of DNA. The specific heat, entropy, and denaturation temperature of the system versus salt concentration are obtained. These results show that the denaturation of DNA not only depends on the temperature but also is influenced by the salt concentration in the solution of DNA, which are in agreement with experimental measurement.展开更多
Ship-mounted container cranes are challenging industrial applications of nonlinear pendulum-like systems with oscillating disturbance which can cause them unstable.Since wave-induced ship motion causes the hoisted con...Ship-mounted container cranes are challenging industrial applications of nonlinear pendulum-like systems with oscillating disturbance which can cause them unstable.Since wave-induced ship motion causes the hoisted container to swing during the transfer operation,the swing motion may be dangerously large and the operation must be stopped.In order to reduce payload pendulation of ship-mounted crane,nonlinear dynamics of ship-mounted crane is derived and a control method using T-S fuzzy model is proposed.Simulation results are given to illustrate the validity of the proposed design method and pendulation of ship-mounted crane is reduced significantly.展开更多
Two rolling ways,unidirectional rolling and cross rolling,were carried out on twin roll cast AZ31 alloy sheet to study the influence of strain path change on the evolution of the rolling microstructure and texture as ...Two rolling ways,unidirectional rolling and cross rolling,were carried out on twin roll cast AZ31 alloy sheet to study the influence of strain path change on the evolution of the rolling microstructure and texture as well as the anisotropic properties of AZ31 alloy sheet with microscopy,X-ray diffraction technique and tensile tests.It is found that cross rolling gives rise to more uniform microstructure and stronger texture intensities compared with unidirectional rolling.The differences in the microstructure and texture intensities are reflected in the anisotropy characterized by the difference in the yield stress and the fracture elongation that were measured along directions in the rolling plane at angles of 0■,45■and 90■from the rolling direction.展开更多
Soliton theory plays an important role in nonlinear physics.The elastic interaction among solitons is oneof the most important properties for integrable systems.In this Letter, an elastic vortex interaction model is p...Soliton theory plays an important role in nonlinear physics.The elastic interaction among solitons is oneof the most important properties for integrable systems.In this Letter, an elastic vortex interaction model is proposed.It is found that the momenta, vortex momenta and the energies of every one vortex and the interaction energies of everytwo vortices are conserved.展开更多
Steel lazy wave catenary riser (SLWR) has been an attractive choice for deepwater oil field developments. However, fatigue is a critical issue in assessing the feasibility of applying SLWR to large motion vessels such...Steel lazy wave catenary riser (SLWR) has been an attractive choice for deepwater oil field developments. However, fatigue is a critical issue in assessing the feasibility of applying SLWR to large motion vessels such as floating production storage and offloading (FPSO) or semi-submersibles. In this work, the time-domain fatigue analysis of SLWR was adopted for better representing the structural nonlinearity, fluid load nonlinearity and riser-soil nonlinear interaction. The Palmgren-Miner rule was employed for the fatigue life prediction along the riser length. The main purpose of this analysis is to present sensitivity analyses of SLWR fatigue life under various input parameters, which include the structural damping, the hydrodynamic coefficients along the riser, the seabed stiffness, the vessel motions, etc. The analyses indicated the strong dependence of the riser fatigue life on these parameters. The results can help designers to understand the dynamic behavior of the SLWR and provide guidance for selection of some critical parameters that are used in the fatigue design.展开更多
Based on the homotopy analysis method, a general analytic technique for strongly nonlinear problems, a Maple package of automated derivation (ADHO) for periodic nonlinear oscillation systems is presented. This Maple...Based on the homotopy analysis method, a general analytic technique for strongly nonlinear problems, a Maple package of automated derivation (ADHO) for periodic nonlinear oscillation systems is presented. This Maple package is valid for periodic oscillation systems in rather general, and can automatically deliver the accurate approximations of the frequency co and the mean of motion δof a nonlinear periodic oscillator. Based on the homotopy analysis method which is valid even for highly nonlinear problems, this Maple package can give accurate approximate expressions even for nonlinear oscillation systems with strong nonlinearity. Besides, the package is user-friendly: One just needs to input a governing equation and initial conditions, and then gets satisfied analytic approximations in few seconds. Several different types of examples are given in this paper to illustrate the validity of this Maple package. Such kind of package provides us a helpful and easy-to-use tool in science and engineering to analyze periodic of this Maple package from the is published publicly. nonlinear oscillations. And it is free address http://numericaltank.sjtu to download the electronic version edu.cn/sjliao.htm once the paper展开更多
China railways track structure II (CRTS II) slab ballastless track on bridge is one kind of track structures unique to China. Its main bearing component of longitudinal force is the continuous base plate rather than ...China railways track structure II (CRTS II) slab ballastless track on bridge is one kind of track structures unique to China. Its main bearing component of longitudinal force is the continuous base plate rather than rail. And the track-bridge interaction is weakened by the sliding layer installed between base plate and bridge deck. In order to study the dynamic response of CRTS II slab ballastless track on bridge under seismic action, a 3D nonlinear dynamic model for simply-supported bridges and CRTS II track was established, which considered structures such as steel rail, fasteners, track plate, mortar layer, base plate, sliding layer, bridge, consolidation, anchors, stoppers, etc. Then its force and deformation features under different intensities of seismic excitation were studied. As revealed, the seismic response of the system increases with the increase of seismic intensity. The peak stresses of rail, track plate and base plate all occur at the abutment or anchors. Both track plate and base plate are about to crack. Besides, the rapid relative displacement between base plate and bridge deck due to the small friction coefficient of sliding layer is beneficial to improve the seismic performance of the system. During the earthquake, a large vertical displacement appears in base plate which leads to frequent collisions between stoppers and base plate, as a result, stoppers may be damaged.展开更多
This paper investigates the nonlinear dynamics of network-based dynamical systems where network communication channels of finite data rates are inserted into the closed loops of the control systems. The authors analyz...This paper investigates the nonlinear dynamics of network-based dynamical systems where network communication channels of finite data rates are inserted into the closed loops of the control systems. The authors analyze the bifurcation and chaotic behavior of the non-smooth dynamical systems. The authors first prove that for almost all system parameters there are no periodic orbits. This result distinguishes this type of non-smooth dynamical systems from many others exhibiting border-collision bifurcations. Next, the authors show analytically that the chaotic sets are separated from the region containing the line segment of all fixed points with a finite distance. Finally, the authors employ a simple model to highlight that both the number of clients sharing a common network channel and fluctuations in the available network bandwidth have significant influence on the performance of such dynamical systems.展开更多
In this article, the authors establish the local null controllability property for semilinear parabolic systems in a domain whose boundary moves in time by a single control force acting on a prescribed subdomain. The ...In this article, the authors establish the local null controllability property for semilinear parabolic systems in a domain whose boundary moves in time by a single control force acting on a prescribed subdomain. The proof is based on Kakutani's fixed point theorem combined with observability estimates for the associated lineaxized system.展开更多
A triad mode resonance, or three-wave resonance, is typical of dynamical systems with quadratic nonlinearities. Suspended cables are found to be rich in triad mode resonant dynamics. In this paper, modulation equation...A triad mode resonance, or three-wave resonance, is typical of dynamical systems with quadratic nonlinearities. Suspended cables are found to be rich in triad mode resonant dynamics. In this paper, modulation equations for cable's triad resonance are formulated by the multiple scale method. Dynamic conservative quantities, i.e., mode energy and Manley-Rowe relations, are then constructed. Equilibrium/dynamic solutions of the modulation equations are obtained, and full investigations into their stability and bifurcation characteristics are presented. Various bifurcation behaviors are detected in cable's triad resonant responses, such as saddle-node, Hopf, pitchfork and period-doubling bifurcations. Nonlinear behaviors, like jump and saturation phenomena, are also found in cable's responses. Based upon the bifurcation analysis, two interesting properties associated with activation of cable's triad resonance are also proposed, i.e., energy barrier and directional dependence. The first gives the critical amplitude of high-frequency mode to activate cable's triad resonance, and the second characterizes the degree of difficulty for activating cable's triad resonance in two opposite directions, i.e., with positive or negative internal detuning parameter.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.10873004the Program for Excellent Talents in Hunan Normal University,the State Key Development Program for Basic Research Program of China under Grant No.2010CB832803+1 种基金the Key project of the National Natural Science Foundation of China under Grant No.10935013Construct Program of the National Key Discipline and the Program for Changjiang Scholars and Innovative Research Team in University under Grant No.IRT0964
文摘In this paper we investigate the scalar field evolution in the dyadosphere spacetime by using the third-order WKB approximation. We find that the coupling term between the gravitation and the nonlinear electrodynamics makes the scalar field decay more quickly and it also makes the scalar field oscillate more slowly. On the o'ther words, this coupling term takes effect on the scalar field evolution as a damping factor. At the same time these effects become more obvious for the scalar field with higher angle quantum number.
文摘This paper describes the dynamic characteristics of pipelines laid through alluvial valleys. We assume that the alluvial valley has a semi-cylindrical cross-section. The ground motion of alluvial valley under harmonic seismic SH waves is carried out, and the pipeline-soil dynamic interaction is taken into account. Though simple, the model may qualitatively explain the earthquake damages of pipelines laid through an alluvial river valley.
基金Foundation item: Supported by the National Natural Science Foundation of China (Grant No. 51079032) and the "111 project" (Grant No. B07019).
文摘Nonlinear interactions among incident wave, tank-sloshing and floating body coupling motion are investigated. The fully nonlinear sloshing and body-surface nonlinear free surface hydrodynamics is simulated using a Non-Uniform Rational B-Spline (NURBS) higher-order panel method in time domain based on the potential theory. A robust and stable improved iterative procedure (Yan and Ma, 2007) for floating bodies is used for calculating the time derivative of velocity potential and floating body motion. An energy dissipation condition based on linear theory adopted by Huang (2011) is developed to consider flow viscosity effects of sloshing flow in nonlinear model. A two-dimensional tank model test was performed to identify its validity. The present nonlinear coupling sway motion results are subsequently compared with the corresponding Rognebakke and Faltinsen (2003)'s experimental results, showing fair agreement. Thus, the numerical approach presented in this paper is expected to be very efficient and realistic in evaluating the coupling effects of nonlinear sloshing and body motion.
基金supported by the China Aerospace Science and Technology Corporation Eighth Research Institute Industry-University-Research Cooperation Fund(No.SAST 2020-019)。
文摘Aiming at the problem of relative navigation for non-cooperative rendezvous of spacecraft,this paper proposes a new angles-only navigation architecture using non-linear dynamics method. This method does not solve the problem of poor observability of angles-only navigation through orbital or attitude maneuvering,but improves the observability of angles-only navigation through capturing the non-linearity of the system in the evolution of relative motion. First,three relative dynamics models and their corresponding line-of-sight(LoS)measurement equations are introduced,including the rectilinear state relative dynamics model,the curvilinear state relative dynamics model,and the relative orbital elements(ROE)state relative dynamics model. Then,an observability analysis theory based on the Gramian matrix is introduced to determine which relative dynamics model could maximize the observability of angles-only navigation. Next,an adaptive extended Kalman filtering scheme is proposed to solve the problem that the angles-only navigation filter using the non-linear dynamics method is sensitive to measurement noises. Finally,the performances of the proposed angles-only navigation architecture are tested by means of numerical simulations,which demonstrates that the angles-only navigation filtering scheme without orbital or attitude maneuvering is completely feasible through improving the modeling of the relative dynamics and LoS measurement equations.
文摘Automatic line reclosing schemes used in an extra-high-voltage power system is an economical and effective means to maintain transient stability. A novel method is proposed in the paper to adaptively optimize the automatic line reclosing time after a transient fault for enhancement of interconnected power system transient stability. Both the study on the transient energy over network and the structure-preserving multi-machines power system model illustrate that the excessive convergence of potential energy on the lines with a certain cutset deteriorate power system stability, and therefore, an optimum line reclosing strategy can be established by minimizing the change in transient potential energy distribution across a cutset lines in the vicinity of the faulty line as an optimization target, and the optimal reclosure time is set to the time of minimum line phase angle difference. Without any pre-determined knowledge, the method is adaptive to various power system operation modes and fault conditions, and easy to implement because only a limited number of data measured at one location on a tie-line linking sub-networks are required. Simulations have been performed with the OMIB(One Machine and Infinite Bus System) and a real inter-connected power system to verify the applicability of the method proposed.
基金Supported by the Foundation of Scientific Research Education and Innovations under Grant No.11609506,Jinan University
文摘We have set up a new reduced model Hamiltonian for the polariton system, in which the nonlinear interaction contains the rotating term k l ( a + b + ab+) and the attractive two-mode squeezed coupling - k2 ( a + b+ + ab ) . The dynamical evolution of this system has been solved and the nonclassical features relevant to the second-order and high-order squeezing have been obtained in an analytical form. For the first time, in contrast to the existing result, we have confirmed for the phonon field that the attractive two-mode squeezed interaction will not only result in the second-order and high-order squeezing in X-component with the time evolution, but also in time average. Furthermore, the phenomena of collapse and revival of inversion will occur as well in the time evolution of the average number of photon and phonon, as also in the second-order and high-order squeezing of photon field, particularly, in the high-order squeezing of phonon field.
基金The project supported by the Doctoral Foundation of the Ministry of Education of China under Grant No.20010614005
文摘We investigate the statistical mechanics properties of a nonlinear dynamics model of the denaturation of the DNA double-helix and study the effects of salt concentration and temperature on denaturation transition of DNA. The specific heat, entropy, and denaturation temperature of the system versus salt concentration are obtained. These results show that the denaturation of DNA not only depends on the temperature but also is influenced by the salt concentration in the solution of DNA, which are in agreement with experimental measurement.
基金work supported by Changwon National University in 2011-2012work partly supported by the second stage of Brain Korea 21 Projects
文摘Ship-mounted container cranes are challenging industrial applications of nonlinear pendulum-like systems with oscillating disturbance which can cause them unstable.Since wave-induced ship motion causes the hoisted container to swing during the transfer operation,the swing motion may be dangerously large and the operation must be stopped.In order to reduce payload pendulation of ship-mounted crane,nonlinear dynamics of ship-mounted crane is derived and a control method using T-S fuzzy model is proposed.Simulation results are given to illustrate the validity of the proposed design method and pendulation of ship-mounted crane is reduced significantly.
基金Project(2007CB613703)supported by the National Basic Research Program of China
文摘Two rolling ways,unidirectional rolling and cross rolling,were carried out on twin roll cast AZ31 alloy sheet to study the influence of strain path change on the evolution of the rolling microstructure and texture as well as the anisotropic properties of AZ31 alloy sheet with microscopy,X-ray diffraction technique and tensile tests.It is found that cross rolling gives rise to more uniform microstructure and stronger texture intensities compared with unidirectional rolling.The differences in the microstructure and texture intensities are reflected in the anisotropy characterized by the difference in the yield stress and the fracture elongation that were measured along directions in the rolling plane at angles of 0■,45■and 90■from the rolling direction.
基金Supported by the National Natural Science Foundation of China under Grant No.10735030 the National Basic Research Programs of China (973 Programs) under Grant Nos.2007CB814800 and 2005CB422301the PCSIRT (IRT0734)
文摘Soliton theory plays an important role in nonlinear physics.The elastic interaction among solitons is oneof the most important properties for integrable systems.In this Letter, an elastic vortex interaction model is proposed.It is found that the momenta, vortex momenta and the energies of every one vortex and the interaction energies of everytwo vortices are conserved.
基金supported by the National Natural Science Foundation of China (Grant Nos. 50739004, 51009093)the Research Fund for the Shandong Province Key Laboratory of Ocean Engineering
文摘Steel lazy wave catenary riser (SLWR) has been an attractive choice for deepwater oil field developments. However, fatigue is a critical issue in assessing the feasibility of applying SLWR to large motion vessels such as floating production storage and offloading (FPSO) or semi-submersibles. In this work, the time-domain fatigue analysis of SLWR was adopted for better representing the structural nonlinearity, fluid load nonlinearity and riser-soil nonlinear interaction. The Palmgren-Miner rule was employed for the fatigue life prediction along the riser length. The main purpose of this analysis is to present sensitivity analyses of SLWR fatigue life under various input parameters, which include the structural damping, the hydrodynamic coefficients along the riser, the seabed stiffness, the vessel motions, etc. The analyses indicated the strong dependence of the riser fatigue life on these parameters. The results can help designers to understand the dynamic behavior of the SLWR and provide guidance for selection of some critical parameters that are used in the fatigue design.
基金supported by the National Science Foundation of China under Grant No.11071274
文摘Based on the homotopy analysis method, a general analytic technique for strongly nonlinear problems, a Maple package of automated derivation (ADHO) for periodic nonlinear oscillation systems is presented. This Maple package is valid for periodic oscillation systems in rather general, and can automatically deliver the accurate approximations of the frequency co and the mean of motion δof a nonlinear periodic oscillator. Based on the homotopy analysis method which is valid even for highly nonlinear problems, this Maple package can give accurate approximate expressions even for nonlinear oscillation systems with strong nonlinearity. Besides, the package is user-friendly: One just needs to input a governing equation and initial conditions, and then gets satisfied analytic approximations in few seconds. Several different types of examples are given in this paper to illustrate the validity of this Maple package. Such kind of package provides us a helpful and easy-to-use tool in science and engineering to analyze periodic of this Maple package from the is published publicly. nonlinear oscillations. And it is free address http://numericaltank.sjtu to download the electronic version edu.cn/sjliao.htm once the paper
基金supported by the National Natural Science Foundation of China (Grant No. 51608542)Project of Science and Technology Research and Development Program of China Railway Corporation (Grant No.2015G001-G)
文摘China railways track structure II (CRTS II) slab ballastless track on bridge is one kind of track structures unique to China. Its main bearing component of longitudinal force is the continuous base plate rather than rail. And the track-bridge interaction is weakened by the sliding layer installed between base plate and bridge deck. In order to study the dynamic response of CRTS II slab ballastless track on bridge under seismic action, a 3D nonlinear dynamic model for simply-supported bridges and CRTS II track was established, which considered structures such as steel rail, fasteners, track plate, mortar layer, base plate, sliding layer, bridge, consolidation, anchors, stoppers, etc. Then its force and deformation features under different intensities of seismic excitation were studied. As revealed, the seismic response of the system increases with the increase of seismic intensity. The peak stresses of rail, track plate and base plate all occur at the abutment or anchors. Both track plate and base plate are about to crack. Besides, the rapid relative displacement between base plate and bridge deck due to the small friction coefficient of sliding layer is beneficial to improve the seismic performance of the system. During the earthquake, a large vertical displacement appears in base plate which leads to frequent collisions between stoppers and base plate, as a result, stoppers may be damaged.
基金supported by an the National Natural Science Foundation of China under Grant No.60804015,and an NSERC grant to the third author
文摘This paper investigates the nonlinear dynamics of network-based dynamical systems where network communication channels of finite data rates are inserted into the closed loops of the control systems. The authors analyze the bifurcation and chaotic behavior of the non-smooth dynamical systems. The authors first prove that for almost all system parameters there are no periodic orbits. This result distinguishes this type of non-smooth dynamical systems from many others exhibiting border-collision bifurcations. Next, the authors show analytically that the chaotic sets are separated from the region containing the line segment of all fixed points with a finite distance. Finally, the authors employ a simple model to highlight that both the number of clients sharing a common network channel and fluctuations in the available network bandwidth have significant influence on the performance of such dynamical systems.
文摘In this article, the authors establish the local null controllability property for semilinear parabolic systems in a domain whose boundary moves in time by a single control force acting on a prescribed subdomain. The proof is based on Kakutani's fixed point theorem combined with observability estimates for the associated lineaxized system.
基金Supporting Program for Young Investigators,Hunan UniversityNational Science Foundation of China(Grant Nos.11502076 and 11572117)
文摘A triad mode resonance, or three-wave resonance, is typical of dynamical systems with quadratic nonlinearities. Suspended cables are found to be rich in triad mode resonant dynamics. In this paper, modulation equations for cable's triad resonance are formulated by the multiple scale method. Dynamic conservative quantities, i.e., mode energy and Manley-Rowe relations, are then constructed. Equilibrium/dynamic solutions of the modulation equations are obtained, and full investigations into their stability and bifurcation characteristics are presented. Various bifurcation behaviors are detected in cable's triad resonant responses, such as saddle-node, Hopf, pitchfork and period-doubling bifurcations. Nonlinear behaviors, like jump and saturation phenomena, are also found in cable's responses. Based upon the bifurcation analysis, two interesting properties associated with activation of cable's triad resonance are also proposed, i.e., energy barrier and directional dependence. The first gives the critical amplitude of high-frequency mode to activate cable's triad resonance, and the second characterizes the degree of difficulty for activating cable's triad resonance in two opposite directions, i.e., with positive or negative internal detuning parameter.