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
We present a specific state variable for a class of fractional-order chaotic systems. By using a specific state variable and its （q-order, 2q-order, ..., and （n-1） q-order） time derivatives, all the state variable...We present a specific state variable for a class of fractional-order chaotic systems. By using a specific state variable and its （q-order, 2q-order, ..., and （n-1） q-order） time derivatives, all the state variables can be obtained. Several fractional-order chaotic systems are used to demonstrate this idea. A hybrid projective synchronization scheme is presented to show its applications.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
The offered book is devoted to theoretical and applied problems of nonlinear dynamics of radio physical systems. The main goal of this book is theoretical and experimental investigations of key principles and laws of ...The offered book is devoted to theoretical and applied problems of nonlinear dynamics of radio physical systems. The main goal of this book is theoretical and experimental investigations of key principles and laws of ra- dio physical system’s functioning with continuous and discrete time, in which both regular and chaotic oscillation types may occur.展开更多
Consider the Cauchy problems for an n-dimensional nonlinear system of fluid dynamics equations. The main purpose of this paper is to improve the Fourier splitting method to accomplish the decay estimates with sharp ra...Consider the Cauchy problems for an n-dimensional nonlinear system of fluid dynamics equations. The main purpose of this paper is to improve the Fourier splitting method to accomplish the decay estimates with sharp rates of the global weak solutions of the Cauchy problems. We will couple togeth- er the elementary uniform energy estimates of the global weak solutions and a well known Gronwall＇s inequality to improve the Fourier splitting method. This method was initiated by Maria Schonbek in the 1980＇s to study the op- timal long time asymptotic behaviours of the global weak solutions of the nonlinear system of fluid dynamics equations. As applications, the decay esti- mates with sharp rates of the global weak solutions of the Cauchy problems for n-dimensional incompressible Navier-Stokes equations, for the n-dimensional magnetohydrodynamics equations and for many other very interesting nonlin- ear evolution equations with dissipations can be established.展开更多
Empirical observations indicate that the interevent time distribution of human actions exhibits heavy-tailed features. The queuing model based on task priorities is to some extent successful in explaining the origin o...Empirical observations indicate that the interevent time distribution of human actions exhibits heavy-tailed features. The queuing model based on task priorities is to some extent successful in explaining the origin of such heavy tails, however, it cannot explain all the temporal statistics of human behavior especially for the daily entertainments. We propose an interest-driven model, which can reproduce the power-law distribution of interevent time. The exponent can be analytically obtained and is in good accordance with the simulations. This model well explains the observed relationship between activities and power-law exponents, as reported recently for web-based behavior and the instant message communications.展开更多
To study the robustness of complex networks under attack and repair, we introduce a repair model of complex networks. Based on the model, we introduce two new quantities, i.e. attack fraction fa and the maximum degree...To study the robustness of complex networks under attack and repair, we introduce a repair model of complex networks. Based on the model, we introduce two new quantities, i.e. attack fraction fa and the maximum degree of the nodes that have never been attacked ~Ka, to study analytically the critical attack fraction and the relative size of the giant component of complex networks under attack and repair, using the method of generating function. We show analytically and numerically that the repair strategy significantly enhances the robustness of the scale-free network and the effect of robustness improvement is better for the scale-free networks with a smaller degree exponent. We discuss the application of our theory in relation to theunderstanding of robustness of complex networks with reparability.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
Unsteady mixed convective boundary layer flow and heat transfer over a stretching vertical surface in the presence of slip axe investigated. It is noted that fluid velocity decreases due to the increasing velocity sli...Unsteady mixed convective boundary layer flow and heat transfer over a stretching vertical surface in the presence of slip axe investigated. It is noted that fluid velocity decreases due to the increasing velocity slip parameter resulting in an increase in the temperature field. The rate of heat transfer decreases with the velocity slip parameter while it increases with unsteadiness parameter. The same feature is also noticed for thermal slip parameter.展开更多
The stochastic resonance （SR） in a time-delayed mono-stable system driven by multiplicative white noise, additive white noise, additive dichotomous noise as well as a periodic square-wave signal is considered from t...The stochastic resonance （SR） in a time-delayed mono-stable system driven by multiplicative white noise, additive white noise, additive dichotomous noise as well as a periodic square-wave signal is considered from the view of the signal-to-noise ratio （SNR）. It is found that the SNR increases monotonically with the increase of the delay time. The SNR exhibits the SR behavior when it is plotted as a function of intensities of the noises, displaying the asymmetry of the dichotomous noise. The SNR varies non-monotonically with the increase of the system parameter and the amplitude of the input square-wave signal.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
In this paper, the nonlinear dynamical behavior of two coupled pipes conveying pulsating fluid is studied. The connection between the two pipes is considered as a distributed linear spring. Based on this consideration...In this paper, the nonlinear dynamical behavior of two coupled pipes conveying pulsating fluid is studied. The connection between the two pipes is considered as a distributed linear spring. Based on this consideration, the equations of motion of the coupled two-pipe system are obtained. The two coupled nonlinear partial differential equations, discretized using the fourth- order Galerkin method, are solved by a fourth-order Runge-Kutta integration algorithm. Results show that the connection stiffness has a significant effect on the dynamical behavior of the coupled system. It is found that for some parameter values the motion types of the two pipes might be synchronous.展开更多
We study an N-dimensional system based upon a sine map, which is related to the simplified model of an opto-electronic system. The system behavior is analyzed with the tools of nonlinear dynamics （bifurcations in the...We study an N-dimensional system based upon a sine map, which is related to the simplified model of an opto-electronic system. The system behavior is analyzed with the tools of nonlinear dynamics （bifurcations in the parameter plane, critical manifolds, basins of attraction, chaotic attractors）. Our study relies on a two-dimensional system （N=2）. It is interesting that this system shows the existence of bounded chaotic orbits, which can be considered for secure transmissions.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
A form of statistical interaction term of one-dimensional anyons is introduced, based on which one-dimensional anyon models are theoretically realized, and the statistical transmutation between bosons （or fermions） ...A form of statistical interaction term of one-dimensional anyons is introduced, based on which one-dimensional anyon models are theoretically realized, and the statistical transmutation between bosons （or fermions） and anyons is established in quantum mechanics formalism. Two kinds of anyon models which are being studied are recovered and reexplained naturally in our formalism.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
Recently, quantitative study on complex systems has become an attractive research area for physicists. Human scientific activity, including scientific paper publication, is an important complex system and therefore de...Recently, quantitative study on complex systems has become an attractive research area for physicists. Human scientific activity, including scientific paper publication, is an important complex system and therefore deserves an investigation. We present a simple model to describe the interaction between journals, authors and editorial board members. In the model the probabilities, with which a journal accepts papers from an author or invites him as an editorial board member, obey normal distributions. However, the most probable value of the latter distribution shifts such that the journal can have higher level authors being its editorial board members. The analytic derivation by the model is in rather good agreement with the empirical observation from the selected fifteen worldwide journals with different impact factors.展开更多
Synchronization behavior of coupled dynamical systems is discussed. An equivalence relation is found between the diffeomorphic generalized synchronization and the complete synchronization of coupled nonidentical syste...Synchronization behavior of coupled dynamical systems is discussed. An equivalence relation is found between the diffeomorphic generalized synchronization and the complete synchronization of coupled nonidentical systems. Employing the method of the complete synchronization, the problem of the generalized synchronization can be unraveled. By constructing an appropriate coupling term, a sufficient condition is obtained for determining the complete synchronization of coupled nonidentical systems. Numerical simulations are also given to show the effectiveness of the proposed schemes.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
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We present a specific state variable for a class of fractional-order chaotic systems. By using a specific state variable and its （q-order, 2q-order, ..., and （n-1） q-order） time derivatives, all the state variables can be obtained. Several fractional-order chaotic systems are used to demonstrate this idea. A hybrid projective synchronization scheme is presented to show its applications.
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.
文摘The offered book is devoted to theoretical and applied problems of nonlinear dynamics of radio physical systems. The main goal of this book is theoretical and experimental investigations of key principles and laws of ra- dio physical system’s functioning with continuous and discrete time, in which both regular and chaotic oscillation types may occur.
文摘Consider the Cauchy problems for an n-dimensional nonlinear system of fluid dynamics equations. The main purpose of this paper is to improve the Fourier splitting method to accomplish the decay estimates with sharp rates of the global weak solutions of the Cauchy problems. We will couple togeth- er the elementary uniform energy estimates of the global weak solutions and a well known Gronwall＇s inequality to improve the Fourier splitting method. This method was initiated by Maria Schonbek in the 1980＇s to study the op- timal long time asymptotic behaviours of the global weak solutions of the nonlinear system of fluid dynamics equations. As applications, the decay esti- mates with sharp rates of the global weak solutions of the Cauchy problems for n-dimensional incompressible Navier-Stokes equations, for the n-dimensional magnetohydrodynamics equations and for many other very interesting nonlin- ear evolution equations with dissipations can be established.
基金Supported by the National Natural Science Foundation of China under Grant Nos 70871082, 10975126, 90924011, 70971089, 10635040 and 60973069, the China Postdoctoral Science Foundation under Grant No 20080431273, and the Sino-Swiss Science and Technology Cooperation （SSSTC） Project （EG 20-032009）. We acknowledge Xiaopu Han and Wei Hong for their useful discussions.
文摘Empirical observations indicate that the interevent time distribution of human actions exhibits heavy-tailed features. The queuing model based on task priorities is to some extent successful in explaining the origin of such heavy tails, however, it cannot explain all the temporal statistics of human behavior especially for the daily entertainments. We propose an interest-driven model, which can reproduce the power-law distribution of interevent time. The exponent can be analytically obtained and is in good accordance with the simulations. This model well explains the observed relationship between activities and power-law exponents, as reported recently for web-based behavior and the instant message communications.
文摘To study the robustness of complex networks under attack and repair, we introduce a repair model of complex networks. Based on the model, we introduce two new quantities, i.e. attack fraction fa and the maximum degree of the nodes that have never been attacked ~Ka, to study analytically the critical attack fraction and the relative size of the giant component of complex networks under attack and repair, using the method of generating function. We show analytically and numerically that the repair strategy significantly enhances the robustness of the scale-free network and the effect of robustness improvement is better for the scale-free networks with a smaller degree exponent. We discuss the application of our theory in relation to theunderstanding of robustness of complex networks with reparability.
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.
文摘Unsteady mixed convective boundary layer flow and heat transfer over a stretching vertical surface in the presence of slip axe investigated. It is noted that fluid velocity decreases due to the increasing velocity slip parameter resulting in an increase in the temperature field. The rate of heat transfer decreases with the velocity slip parameter while it increases with unsteadiness parameter. The same feature is also noticed for thermal slip parameter.
文摘The stochastic resonance （SR） in a time-delayed mono-stable system driven by multiplicative white noise, additive white noise, additive dichotomous noise as well as a periodic square-wave signal is considered from the view of the signal-to-noise ratio （SNR）. It is found that the SNR increases monotonically with the increase of the delay time. The SNR exhibits the SR behavior when it is plotted as a function of intensities of the noises, displaying the asymmetry of the dichotomous noise. The SNR varies non-monotonically with the increase of the system parameter and the amplitude of the input square-wave signal.
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Project supported by the National Natural Science Foundation of China(Nos.11172107 and 11172109)the Program for New Century Excellent Talents in University(No.NCET-11-0183)
文摘In this paper, the nonlinear dynamical behavior of two coupled pipes conveying pulsating fluid is studied. The connection between the two pipes is considered as a distributed linear spring. Based on this consideration, the equations of motion of the coupled two-pipe system are obtained. The two coupled nonlinear partial differential equations, discretized using the fourth- order Galerkin method, are solved by a fourth-order Runge-Kutta integration algorithm. Results show that the connection stiffness has a significant effect on the dynamical behavior of the coupled system. It is found that for some parameter values the motion types of the two pipes might be synchronous.
基金Supported by the National Science Fund for Distinguished Young Scholars under Grant No 60725104, the National Basic Research Program of China under Grant No 2007CB310706, the National High-Technology Research and Development Program of China under Grant Nos 2008AA01Z447, 2008AA011002 and 2009AA01Z215, the National Natural Science Foundation of China under Grant Nos 60873263, 60932002 and 60932005, the Research Fund for the Doctoral Program of Higher Education under Grant No 20060614018, Youth Foundation of University of Electronic Science and Technology of China under Grant No L0801010jx0815, and the French Project ANR05RNRT02001 ACSCOM.
文摘We study an N-dimensional system based upon a sine map, which is related to the simplified model of an opto-electronic system. The system behavior is analyzed with the tools of nonlinear dynamics （bifurcations in the parameter plane, critical manifolds, basins of attraction, chaotic attractors）. Our study relies on a two-dimensional system （N=2）. It is interesting that this system shows the existence of bounded chaotic orbits, which can be considered for secure transmissions.
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 National Natural Science Foundation of China under Grant No 10947138, and in part by the Research Foundation of Anhui Normal University under Grant No 2009xqn63.
文摘A form of statistical interaction term of one-dimensional anyons is introduced, based on which one-dimensional anyon models are theoretically realized, and the statistical transmutation between bosons （or fermions） and anyons is established in quantum mechanics formalism. Two kinds of anyon models which are being studied are recovered and reexplained naturally in our formalism.
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.
基金Supported by the National Natural Science Foundation of China under grant Nos 10635040, 70671089 and 10705023.
文摘Recently, quantitative study on complex systems has become an attractive research area for physicists. Human scientific activity, including scientific paper publication, is an important complex system and therefore deserves an investigation. We present a simple model to describe the interaction between journals, authors and editorial board members. In the model the probabilities, with which a journal accepts papers from an author or invites him as an editorial board member, obey normal distributions. However, the most probable value of the latter distribution shifts such that the journal can have higher level authors being its editorial board members. The analytic derivation by the model is in rather good agreement with the empirical observation from the selected fifteen worldwide journals with different impact factors.
基金Supported by the National Science Foundation for Distinguished Young Scholars of China under Grant No 10425209, the National Natural Science Foundation of China under Grant No 10972011, the China Postdoctoral Science Foundation under Grant No 20080430295, the Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality.
文摘Synchronization behavior of coupled dynamical systems is discussed. An equivalence relation is found between the diffeomorphic generalized synchronization and the complete synchronization of coupled nonidentical systems. Employing the method of the complete synchronization, the problem of the generalized synchronization can be unraveled. By constructing an appropriate coupling term, a sufficient condition is obtained for determining the complete synchronization of coupled nonidentical systems. Numerical simulations are also given to show the effectiveness of the proposed schemes.
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.
