A large class of partial differential equations in the modelling of ocean waves are due to Ostrovsky. We determine the invariance properties （through the Lie point symmetry generators） and construct classes of conse...A large class of partial differential equations in the modelling of ocean waves are due to Ostrovsky. We determine the invariance properties （through the Lie point symmetry generators） and construct classes of conservation laws for some of the models. In the latter case, the method involves finding the ＇multipliers＇ associated with the conservation laws with a stronger emphasis on the ＇higher-order＇ ones. The relationship between the symmetries and conservation laws is investigated by considering the invariance properties of the multipliers.展开更多
Topology identification is an important problem for complex networks because much information about networks in practice such as the topological structure is uncertain. We propose an adaptive control method for identi...Topology identification is an important problem for complex networks because much information about networks in practice such as the topological structure is uncertain. We propose an adaptive control method for identifying the topology of general nonlinearly-coupled complex network models that are either non-delayed or delayed coupled. Simulation results are also presented to illustrate the effectiveness of the method.展开更多
A two-degree-of-freedom model of iced, electrical quad bundle conductor is developed to comprehensively describe the different galloping behaviors observed. By applying centre manifold and invertible linear transforma...A two-degree-of-freedom model of iced, electrical quad bundle conductor is developed to comprehensively describe the different galloping behaviors observed. By applying centre manifold and invertible linear transformation, the co-dimension-2 bifurcation is analyzed. The relationships of parameters between this system and the original system are obtained to analyze and to control the galloping of the quad iced bundle conductor. The space trajectory, Lyapunov exponent and Lyapunov dimension are investigated via numerical simulation to present a rigorous proof of existence of chaos.展开更多
A new generalized Lorenz system is presented based on the thermal convection of Oldroyd-B fluids in a circular loop. Two non-dimensional parameters De1 （a measure of the fluid relaxation） and De2 （a measure of the ...A new generalized Lorenz system is presented based on the thermal convection of Oldroyd-B fluids in a circular loop. Two non-dimensional parameters De1 （a measure of the fluid relaxation） and De2 （a measure of the fluid retardation） appear in the equation. Then we study this generalized Lorenz equation numerically and find that the values of De1 and De2 can greatly influence the behavior of the solution. The fluid relaxation De1 is found to precipitate the onset of periodic solution （limit cycle） in the system and impedes the onset of chaos while the fluid retardation （De2） tends to delay the onset of the periodic solution and precipitate the onset of chaos in the system.展开更多
We mainly investigate the issues of fuzzy modeling and impulsive control of a memristor-based chaotic system and present a memristor-based chaotic system as the Takagi-Sugeno model-based fuzzy system. Then, based on t...We mainly investigate the issues of fuzzy modeling and impulsive control of a memristor-based chaotic system and present a memristor-based chaotic system as the Takagi-Sugeno model-based fuzzy system. Then, based on the impulsive control theory of dynamical systems, a criterion ensuring impulsive stabilization of the memristorbased chaotic system is derived for the first time. An illustrative example is given to verify the effectiveness of the control scheme.展开更多
Considering corrections to all orders in the Planck length on the quantum state density from the generalized uncertainty principle and using the quantum state density to all degrees of freedom including extra dimensio...Considering corrections to all orders in the Planck length on the quantum state density from the generalized uncertainty principle and using the quantum state density to all degrees of freedom including extra dimensions, we calculate the statistical entropy of the scalar field in the higher-dimensional static spherically symmetric black hole spacetime without any artificial cutoff. Calculation shows that the entropy is proportional to the horizon area. The coefficient of proportionality is 1/4 when the minimal length parameter is selected appropriately.展开更多
It is demonstrated by the linear modulational instability analysis that a generalized （2＋1）-dimensional Hirota equation is modulationally stable. Then, a B？cklund transformation （BT） is obtained by means of the ...It is demonstrated by the linear modulational instability analysis that a generalized （2＋1）-dimensional Hirota equation is modulationally stable. Then, a B？cklund transformation （BT） is obtained by means of the truncated Painlevé approach. Using the BT, the model is transformed to a system of equations, which finally leads to a special variable separation solution with arbitrary functions.展开更多
We demonstrate that the projective synchronization can be observed in coupled fractional-order chaotic systems. A new systematic and powerful coupling scheme is developed to investigate the projective synchronization ...We demonstrate that the projective synchronization can be observed in coupled fractional-order chaotic systems. A new systematic and powerful coupling scheme is developed to investigate the projective synchronization via the open-plus-closed-loop control, which allows us to arbitrarily manipulate the scaling factor of projective synchronization. The proposed scheme is proved analytically on the basis of the stability theorem of the fractional differential equations. Numerical simulations on the fraction-order chaotic Chen system are presented to justify the theoretical analysis.展开更多
Bilinear forms and double-Wronskian solutions are given for two hierarchies, the （2＋1）-dimensional breaking Ablowitz-Kaup-Newell-Segur （AKNS） hierarchy and the negative order AKNS hierarchy. According to some cho...Bilinear forms and double-Wronskian solutions are given for two hierarchies, the （2＋1）-dimensional breaking Ablowitz-Kaup-Newell-Segur （AKNS） hierarchy and the negative order AKNS hierarchy. According to some choices of the coefficient matrix in the Wronskian condition equation set, we obtain some kinds of solutions for these two hierarchies, such as solitons, 3ordan block solutions, rational solutions, complexitons and mixed solutions.展开更多
Considering the TDFC controlled current-mode Buck converter featuring periodicity we propose a Fourier-decomposition based method for the bifurcation analysis of this system, hence the theoretical range of control gai...Considering the TDFC controlled current-mode Buck converter featuring periodicity we propose a Fourier-decomposition based method for the bifurcation analysis of this system, hence the theoretical range of control gain of TDFC is determined. In addition, the power-stage experiment circuit is built and the control part is realized in a digital controller. The experimental results show that either bifurcation or chaos in the current-mode Buck converter can be controlled into the expectant period-1 orbit rapidly.展开更多
A new fractional-order Lorenz system is obtained from the convection of fractional Maxwell fluids in a circular loop. This is the first fractional-order dynamical system derived from an actual physical problem, and ri...A new fractional-order Lorenz system is obtained from the convection of fractional Maxwell fluids in a circular loop. This is the first fractional-order dynamical system derived from an actual physical problem, and rich dynamical properties are observed. In the case of short fluid relaxation time, with the decreasing effective dimension ∑, we find a critical value of the effective dimension ∑cr1, at which the solution of the system undergoes a transition from the chaotic motion to the periodic motion and another critical value ∑cr2（∑cr2 〈∑cr1） at which the regular dynamics of the system returns to the chaotic one. In the case of long relaxation time, the phenomenon of overstability is observed and the decrease of ∑ is found to delay the onset of it.展开更多
Conjectures are made for the ground state energy of a large spin 1/2 Fermion system trapped in a 1D harmonic trap with delta function interaction. States with different spin J are separately studied. The Thomas-Fermi ...Conjectures are made for the ground state energy of a large spin 1/2 Fermion system trapped in a 1D harmonic trap with delta function interaction. States with different spin J are separately studied. The Thomas-Fermi method is used as an effective test for the conjecture.展开更多
By the density-functional calculation we investigate the ground-state properties of Bose-Fermi mixture confined in one-dimensional harmonic traps. The homogeneous mixture of bosons and polarized fermions with contact ...By the density-functional calculation we investigate the ground-state properties of Bose-Fermi mixture confined in one-dimensional harmonic traps. The homogeneous mixture of bosons and polarized fermions with contact interaction can be exactly solved by the Bethe-ansatz method. After giving the exact formula of ground state en- ergy density, we employ the local-density approximation to determine the density distribution of each component. It is shown that with the increase in interaction, the total density distribution evolves to Fermi-like distribution and the system exhibits phase separation between finite. While in the infinite interaction limit both distributions and phase separation disappears. two components when the interaction is strong enough but bosons and fermions display the completely same Fermi-like展开更多
Chaotic thermal convection in a rapidly rotating cylindrical annulus is investigated numerically and the relaxation oscillation state is obtained under the no-slip boundary condition. The dominant frequency of the osc...Chaotic thermal convection in a rapidly rotating cylindrical annulus is investigated numerically and the relaxation oscillation state is obtained under the no-slip boundary condition. The dominant frequency of the oscillation is inherited directly from a vacillating mode, whose nonlinear interaction with another high-frequency vacillating mode leads to the chaotic state at high Rayleigh numbers through an RTN-type route. Furthermore, the effects of Coriolis parameter and Rayleigh number on the quasi-periodic burst of kinetic energy are discussed as well.展开更多
For M×N spectral matrix, a kind of operation ？ which satisfies combination law （a？b）？c=a？（b？c） is introduced. The discrete multi？component zero-curvature equation is deduced by using the new operation ...For M×N spectral matrix, a kind of operation ？ which satisfies combination law （a？b）？c=a？（b？c） is introduced. The discrete multi？component zero-curvature equation is deduced by using the new operation ？, and a simple method for constructing discrete multi-component integrable hierarchy is proposed. As its application, the multi-component Toda hierarchy and its two kinds of integrable couplings are worked out.展开更多
An innovative theoretical framework for stochastic dynamics based on the decomposition of a stochas- tic differential equation （SDE） into a dissipative component, a detailed-balance-breaking component, and a dual-ro...An innovative theoretical framework for stochastic dynamics based on the decomposition of a stochas- tic differential equation （SDE） into a dissipative component, a detailed-balance-breaking component, and a dual-role potential landscape has been developed, which has fruitful applications in physics, engineering, chemistry, and biology. It introduces the A-type stochastic interpretation of the SDE beyond the traditional Ito or Stratonovich interpretation or even the a-type interpretation for multi- dimensional systems. The potential landscape serves as a Hmniltonian-like function in nonequilibrimn processes without detailed balance, which extends this important concept from equilibrium statistical physics to the nonequilibrium region. A question on the uniqueness of the SDE decomposition was recently raised. Our review of both the mathematical and physical aspects shows that uniqueness is guaranteed. The demonstration leads to a better understanding of the robustness of the novel frame- work. In addition, we discuss related issues including the limitations of an approach to obtaining the potential function from a steady-state distribution.展开更多
文摘A large class of partial differential equations in the modelling of ocean waves are due to Ostrovsky. We determine the invariance properties （through the Lie point symmetry generators） and construct classes of conservation laws for some of the models. In the latter case, the method involves finding the ＇multipliers＇ associated with the conservation laws with a stronger emphasis on the ＇higher-order＇ ones. The relationship between the symmetries and conservation laws is investigated by considering the invariance properties of the multipliers.
文摘Topology identification is an important problem for complex networks because much information about networks in practice such as the topological structure is uncertain. We propose an adaptive control method for identifying the topology of general nonlinearly-coupled complex network models that are either non-delayed or delayed coupled. Simulation results are also presented to illustrate the effectiveness of the method.
基金Supported by the National Natural Science Foundation of China under Grant No 10872141, and the National Basic Research Program of China under Grant No 2007CB714000.
文摘A two-degree-of-freedom model of iced, electrical quad bundle conductor is developed to comprehensively describe the different galloping behaviors observed. By applying centre manifold and invertible linear transformation, the co-dimension-2 bifurcation is analyzed. The relationships of parameters between this system and the original system are obtained to analyze and to control the galloping of the quad iced bundle conductor. The space trajectory, Lyapunov exponent and Lyapunov dimension are investigated via numerical simulation to present a rigorous proof of existence of chaos.
基金Supported by the National Natural Science Foundation of China under Grant No 10972117.
文摘A new generalized Lorenz system is presented based on the thermal convection of Oldroyd-B fluids in a circular loop. Two non-dimensional parameters De1 （a measure of the fluid relaxation） and De2 （a measure of the fluid retardation） appear in the equation. Then we study this generalized Lorenz equation numerically and find that the values of De1 and De2 can greatly influence the behavior of the solution. The fluid relaxation De1 is found to precipitate the onset of periodic solution （limit cycle） in the system and impedes the onset of chaos while the fluid retardation （De2） tends to delay the onset of the periodic solution and precipitate the onset of chaos in the system.
文摘We mainly investigate the issues of fuzzy modeling and impulsive control of a memristor-based chaotic system and present a memristor-based chaotic system as the Takagi-Sugeno model-based fuzzy system. Then, based on the impulsive control theory of dynamical systems, a criterion ensuring impulsive stabilization of the memristorbased chaotic system is derived for the first time. An illustrative example is given to verify the effectiveness of the control scheme.
基金Supported by the Graduate Student Creative Foundation of Hunan University of Science and Technology under Grant No S080111, Scientific Research Foundation for the Returned Overseas Chinese Scholars from State Education Ministry of China under Grant No 527[2004]） and the Hunan Provincial Natural Science Foundation under Grant No 06JJ2026.
文摘Considering corrections to all orders in the Planck length on the quantum state density from the generalized uncertainty principle and using the quantum state density to all degrees of freedom including extra dimensions, we calculate the statistical entropy of the scalar field in the higher-dimensional static spherically symmetric black hole spacetime without any artificial cutoff. Calculation shows that the entropy is proportional to the horizon area. The coefficient of proportionality is 1/4 when the minimal length parameter is selected appropriately.
基金Supported by the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No 20070248120, SRF for ROCS, SEM, and the National Natural Science Foundation of China under Grant Nos 10735030 and 10905038.
文摘It is demonstrated by the linear modulational instability analysis that a generalized （2＋1）-dimensional Hirota equation is modulationally stable. Then, a B？cklund transformation （BT） is obtained by means of the truncated Painlevé approach. Using the BT, the model is transformed to a system of equations, which finally leads to a special variable separation solution with arbitrary functions.
基金Supported by the National Natural Science Foundation of China under Grant Nos 10871074 and 60704045, Research and for the Doctoral Program of Higher Education of China under Grant No 20070558053, and the Natural Science Foundation of Guangdong Province under Grant No 9451042001004076.
文摘We demonstrate that the projective synchronization can be observed in coupled fractional-order chaotic systems. A new systematic and powerful coupling scheme is developed to investigate the projective synchronization via the open-plus-closed-loop control, which allows us to arbitrarily manipulate the scaling factor of projective synchronization. The proposed scheme is proved analytically on the basis of the stability theorem of the fractional differential equations. Numerical simulations on the fraction-order chaotic Chen system are presented to justify the theoretical analysis.
基金Supported by the National Natural Science Foundation of China under Grant Nos 10671121 and 10926036, and the Shanghai Leading Academic Discipline Project （J50101）.
文摘Bilinear forms and double-Wronskian solutions are given for two hierarchies, the （2＋1）-dimensional breaking Ablowitz-Kaup-Newell-Segur （AKNS） hierarchy and the negative order AKNS hierarchy. According to some choices of the coefficient matrix in the Wronskian condition equation set, we obtain some kinds of solutions for these two hierarchies, such as solitons, 3ordan block solutions, rational solutions, complexitons and mixed solutions.
基金Supported by the National Natural Science Foundation of China under Grant Nos 50807058 and 50907076 and the Scientific Research Foundation of State Key Lab of Power Transmission Equipment and System Security （2007DA10512708205）.
文摘Considering the TDFC controlled current-mode Buck converter featuring periodicity we propose a Fourier-decomposition based method for the bifurcation analysis of this system, hence the theoretical range of control gain of TDFC is determined. In addition, the power-stage experiment circuit is built and the control part is realized in a digital controller. The experimental results show that either bifurcation or chaos in the current-mode Buck converter can be controlled into the expectant period-1 orbit rapidly.
基金Supported by the National Natural Science Foundation of China under Grant No 10972117.
文摘A new fractional-order Lorenz system is obtained from the convection of fractional Maxwell fluids in a circular loop. This is the first fractional-order dynamical system derived from an actual physical problem, and rich dynamical properties are observed. In the case of short fluid relaxation time, with the decreasing effective dimension ∑, we find a critical value of the effective dimension ∑cr1, at which the solution of the system undergoes a transition from the chaotic motion to the periodic motion and another critical value ∑cr2（∑cr2 〈∑cr1） at which the regular dynamics of the system returns to the chaotic one. In the case of long relaxation time, the phenomenon of overstability is observed and the decrease of ∑ is found to delay the onset of it.
基金Partly supported by the National Natural Science Foundation of China under Grants Nos 10847002, J0825002, and 10675050.
文摘Conjectures are made for the ground state energy of a large spin 1/2 Fermion system trapped in a 1D harmonic trap with delta function interaction. States with different spin J are separately studied. The Thomas-Fermi method is used as an effective test for the conjecture.
基金Supported by the National Natural Science Foundation of China under Grants No 11004007, and the Fundamental Research Funds for the Central Universities under Grant No 06108019.
文摘By the density-functional calculation we investigate the ground-state properties of Bose-Fermi mixture confined in one-dimensional harmonic traps. The homogeneous mixture of bosons and polarized fermions with contact interaction can be exactly solved by the Bethe-ansatz method. After giving the exact formula of ground state en- ergy density, we employ the local-density approximation to determine the density distribution of each component. It is shown that with the increase in interaction, the total density distribution evolves to Fermi-like distribution and the system exhibits phase separation between finite. While in the infinite interaction limit both distributions and phase separation disappears. two components when the interaction is strong enough but bosons and fermions display the completely same Fermi-like
基金Supported by the National Natural Science Foundation of China under Grant Nos 10672003 and 10972007.
文摘Chaotic thermal convection in a rapidly rotating cylindrical annulus is investigated numerically and the relaxation oscillation state is obtained under the no-slip boundary condition. The dominant frequency of the oscillation is inherited directly from a vacillating mode, whose nonlinear interaction with another high-frequency vacillating mode leads to the chaotic state at high Rayleigh numbers through an RTN-type route. Furthermore, the effects of Coriolis parameter and Rayleigh number on the quasi-periodic burst of kinetic energy are discussed as well.
基金Supported by the National Basic Research Program of China （2007CB814800）, the National Natural Science Foundation of China （10901090 and 10801083）, and Chinese Universities Scientific Fund （2009JS42 and 2009-2-05）.
文摘For M×N spectral matrix, a kind of operation ？ which satisfies combination law （a？b）？c=a？（b？c） is introduced. The discrete multi？component zero-curvature equation is deduced by using the new operation ？, and a simple method for constructing discrete multi-component integrable hierarchy is proposed. As its application, the multi-component Toda hierarchy and its two kinds of integrable couplings are worked out.
基金This work was supported in part by the National Natural Science Foundation of China （Grant Nos. NSFC91329301 and NSFC9152930016） and grants from the State Key Laboratory of Oncogenes and Related Genes （Grant No. 90-10-11）.
文摘An innovative theoretical framework for stochastic dynamics based on the decomposition of a stochas- tic differential equation （SDE） into a dissipative component, a detailed-balance-breaking component, and a dual-role potential landscape has been developed, which has fruitful applications in physics, engineering, chemistry, and biology. It introduces the A-type stochastic interpretation of the SDE beyond the traditional Ito or Stratonovich interpretation or even the a-type interpretation for multi- dimensional systems. The potential landscape serves as a Hmniltonian-like function in nonequilibrimn processes without detailed balance, which extends this important concept from equilibrium statistical physics to the nonequilibrium region. A question on the uniqueness of the SDE decomposition was recently raised. Our review of both the mathematical and physical aspects shows that uniqueness is guaranteed. The demonstration leads to a better understanding of the robustness of the novel frame- work. In addition, we discuss related issues including the limitations of an approach to obtaining the potential function from a steady-state distribution.
