The ice accretion on the wing surface of aircraft significantly impacts flight safety.Providing a precise safety assessment by examining flight characteristics and meteorological conditions is challenging.Based on dif...The ice accretion on the wing surface of aircraft significantly impacts flight safety.Providing a precise safety assessment by examining flight characteristics and meteorological conditions is challenging.Based on different swept angles,the experimental data from the icing wind tunnel establish the geometric link between the position of the wingspan and the shape of ice accretion at the leading edge.The correlation analysis and Sobol sensitivity are used to study the uncertainty of single variable.Simultaneously,the polynomial chaos method is employed to study the uncertainty of multiple variables.The results indicate significant correlation between the angle of attack and lift and drag coefficients.The influence of height and velocity on sensitivity is negligible,with the aerodynamic characteristics mostly dependent on the geometric attributes of the ice structure.The uncertainty propagation framework established can accurately assess the impact of swept angle on the aerodynamic parameters of the icing wing,and the predicted findings fall within a 95%confidence interval.展开更多
在某些特殊条件下,电力系统会受影响产生混沌振荡现象,影响电网的安全稳定运行。比如,电力系统在运行过程中产生过多的无功功率将会导致电压相角偏移,从而进一步引发电力系统混沌振荡现象。通过对电力系统相对电角度和相对角速度的调控...在某些特殊条件下,电力系统会受影响产生混沌振荡现象,影响电网的安全稳定运行。比如,电力系统在运行过程中产生过多的无功功率将会导致电压相角偏移,从而进一步引发电力系统混沌振荡现象。通过对电力系统相对电角度和相对角速度的调控和观测,可以实现电力系统稳定性的控制。文中首先对二阶电力系统模型(model of second order power system, MSOPS)进行混沌振荡的动力学分析,综合利用反步法和固定时间控制器等方法,设计了一种改进有限时间(finite-time, FT)的控制器,既实现了对电力系统混沌振荡的抑制又减轻了计算负担、提升系统收敛速度。最后采用MATLAB软件进行数值仿真表明:文中提出的控制策略能够快速抑制电力系统的混沌状态,验证了控制方法的鲁棒性和快速性。展开更多
To overcome excessive computation errors and convergence failures encountered in an iterative calculation of the reliability index using the response surface method （RSM） for some nonlinear limit state functions, th...To overcome excessive computation errors and convergence failures encountered in an iterative calculation of the reliability index using the response surface method （RSM） for some nonlinear limit state functions, this study investigates an essential factor based on chaotic dynamics theory. The bifurcation diagrams of the reliability index are presented for some typical nonlinear limit state functions, and the computation results from the mapping functions due to the RSM iterations show the complicated dynamic phenomena such as the periodic oscillation, as well as bifurcation and chaos. From the numerical examples, it is concluded that the parameter of selection range fplays an important role in the convergence of the RSM iteration, and an improved RSM iterative algorithm is proposed with regard to the incorporation of the iterative sequential function of selection rangef The proposed method is shown to be efficient and to yield accurate results.展开更多
Global bifurcations and multi-pulse chaotic dynamics for a simply supported rectangular thin plate are studied by the extended Melnikov method. The rectangular thin plate is subject to transversal and in-plane excitat...Global bifurcations and multi-pulse chaotic dynamics for a simply supported rectangular thin plate are studied by the extended Melnikov method. The rectangular thin plate is subject to transversal and in-plane excitation. A two-degree-of-freedom nonlinear nonautonomous system governing equations of motion for the rectangular thin plate is derived by the von Karman type equation and the Galerkin approach. A one-to- one internal resonance is considered. An averaged equation is obtained with a multi-scale method. After transforming the averaged equation into a standard form, the extended Melnikov method is used to show the existence of multi-pulse chaotic dynamics, which can be used to explain the mechanism of modal interactions of thin plates. A method for calculating the Melnikov function is given without an explicit analytical expression of homoclinic orbits. Furthermore, restrictions on the damping, excitation, and detuning parameters are obtained, under which the multi-pulse chaotic dynamics is expected. The results of numerical simulations are also given to indicate the existence of small amplitude multi-pulse chaotic responses for the rectangular thin plate.展开更多
This paper investigates synchronization within the new systems, which we denote as Liu system in this paper. New stability criteria for synchronization of linearly coupled Liu systems are attained using the Lyapunov m...This paper investigates synchronization within the new systems, which we denote as Liu system in this paper. New stability criteria for synchronization of linearly coupled Liu systems are attained using the Lyapunov method. Some sufficient conditions for synchronization are concluded through rigorous mathematical theory, which can be further applied to more chaotic systems. Moreover, numerical simulations are given to show the effectiveness of our synchronization criterions.展开更多
This paper proposes an adaptive parameter identification method for breaking chaotic shift key communication from the transmitted signal in public channel. The sensitive dependence property of chaos on parameter misma...This paper proposes an adaptive parameter identification method for breaking chaotic shift key communication from the transmitted signal in public channel. The sensitive dependence property of chaos on parameter mismatch is used for chaos adaptive synchronization and parameter identification. An index function about the synchronization error is defined and conjugate gradient method is used to minimize the index function and to search the transmitter＇s parameter （key）. By using proposed method, secure key is recovered from transmitted signal generated by low dimensional chaos and hyper chaos switching communication. Multi-parameters can also be identified from the transmitted signal with noise.展开更多
This paper studies chaotic motions in quasi-integrable Hamiltonian systems with slow-varying parameters under both harmonic and noise excitations. Based on the dynamic theory and some assumptions of excited noises, an...This paper studies chaotic motions in quasi-integrable Hamiltonian systems with slow-varying parameters under both harmonic and noise excitations. Based on the dynamic theory and some assumptions of excited noises, an extended form of the stochastic Melnikov method is presented. Using this extended method, the homoclinic bifurcations and chaotic behavior of a nonlinear Hamiltonian system with weak feed-back control under both harmonic and Gaussian white noise excitations are analyzed in detail. It is shown that the addition of stochastic excitations can make the parameter threshold value for the occurrence of chaotic motions vary in a wider region. Therefore, chaotic motions may arise easily in the system. By the Monte-Carlo method, the numerical results for the time-history and the maximum Lyapunov exponents of an example system are finally given to illustrate that the presented method is effective.展开更多
In this paper, we investigate the problem of H∞ synchronization for chaotic neural networks with time-varying delays. A new model of the networks with disturbances in both master and slave systems is presented. By co...In this paper, we investigate the problem of H∞ synchronization for chaotic neural networks with time-varying delays. A new model of the networks with disturbances in both master and slave systems is presented. By constructing a suitable Lyapunov–Krasovskii functional and using a reciprocally convex approach, a novel H∞ synchronization criterion for the networks concerned is established in terms of linear matrix inequalities （LMIs） which can be easily solved by various effective optimization algorithms. Two numerical examples are given to illustrate the effectiveness of the proposed method.展开更多
This paper is concerned with the Hopf bifurcation control of a modified Pan-like chaotic system. Based on the Routh-Hurwtiz theory and high-dimensional Hopf bifurcation theory, the existence and stability of the Hopf ...This paper is concerned with the Hopf bifurcation control of a modified Pan-like chaotic system. Based on the Routh-Hurwtiz theory and high-dimensional Hopf bifurcation theory, the existence and stability of the Hopf bifurcation depending on selected values of the system parameters are studied. The region of the stability for the Hopf bifurcation is investigated.By the hybrid control method, a nonlinear controller is designed for changing the Hopf bifurcation point and expanding the range of the stability. Discussions show that with the change of parameters of the controller, the Hopf bifurcation emerges at an expected location with predicted properties and the range of the Hopf bifurcation stability is expanded. Finally,numerical simulation is provided to confirm the analytic results.展开更多
The nonlinear dynamical equations of axle symmetry are established by the method of quasi-shells for three-dimensional shallow conical single-layer lattice shells. The compatible equations are given in geometrical non...The nonlinear dynamical equations of axle symmetry are established by the method of quasi-shells for three-dimensional shallow conical single-layer lattice shells. The compatible equations are given in geometrical nonlinear range. A nonlinear differential equation containing the second and the third order nonlinear items is derived under the boundary conditions of fixed and clamped edges by the method of Galerkin. The problem of bifurcation is discussed by solving the Floquet exponent. In order to study chaotic motion, the equations of free oscillation of a kind of nonlinear dynamics system are solved. Then an exact solution to nonlinear free oscillation of the shallow conical single-layer lattice shell is found as well. The critical conditions of chaotic motion are obtained by solving Melnikov functions, some phase planes are drawn by using digital simulation proving the existence of chaotic motion.展开更多
This work presents the complexity that emerges in a Bertrand duopoly between two companies in the Greek oil market, one of which is semi-public and the other is private. The game uses linear demand functions for diffe...This work presents the complexity that emerges in a Bertrand duopoly between two companies in the Greek oil market, one of which is semi-public and the other is private. The game uses linear demand functions for differentiated products from the existing literature and asymmetric cost functions that arose after approaches using the published financial reports of the two oil companies (Hellenic Petroleum and Motor Oil). The game is based on the assumption of homogeneous players who are characterized by bounded rationality and follow an adjustment mechanism. The players’ decisions for each time period are expressed by two difference equations. A dynamical analysis of the game’s discrete dynamical system is made by finding the equilibrium positions and studying their stability. Numerical simulations include bifurcation diagrams and strange attractors. Lyapunov numbers’ graphs and sensitivity analysis in initial conditions prove the algebraic results and reveal the complexity and chaotic behavior of the system focusing on the two parameters k<sub>1</sub> and k<sub>2</sub> (speed of adjustment for each player). The d-Backtest method is applied through which an attempt is made to control the chaos that appears outside the stability space in order to return to the locally asymptotically stable Nash equilibrium for the system.展开更多
基金supported by the National Natural Science Foundation of China(No.92371201)the State Key Laboratory for Strength and Vibration of Mechanical Structures Program,China.Thanks to China Aerodynamics Research and Development Center for providing the experimental data.
文摘The ice accretion on the wing surface of aircraft significantly impacts flight safety.Providing a precise safety assessment by examining flight characteristics and meteorological conditions is challenging.Based on different swept angles,the experimental data from the icing wind tunnel establish the geometric link between the position of the wingspan and the shape of ice accretion at the leading edge.The correlation analysis and Sobol sensitivity are used to study the uncertainty of single variable.Simultaneously,the polynomial chaos method is employed to study the uncertainty of multiple variables.The results indicate significant correlation between the angle of attack and lift and drag coefficients.The influence of height and velocity on sensitivity is negligible,with the aerodynamic characteristics mostly dependent on the geometric attributes of the ice structure.The uncertainty propagation framework established can accurately assess the impact of swept angle on the aerodynamic parameters of the icing wing,and the predicted findings fall within a 95%confidence interval.
文摘在某些特殊条件下,电力系统会受影响产生混沌振荡现象,影响电网的安全稳定运行。比如,电力系统在运行过程中产生过多的无功功率将会导致电压相角偏移,从而进一步引发电力系统混沌振荡现象。通过对电力系统相对电角度和相对角速度的调控和观测,可以实现电力系统稳定性的控制。文中首先对二阶电力系统模型(model of second order power system, MSOPS)进行混沌振荡的动力学分析,综合利用反步法和固定时间控制器等方法,设计了一种改进有限时间(finite-time, FT)的控制器,既实现了对电力系统混沌振荡的抑制又减轻了计算负担、提升系统收敛速度。最后采用MATLAB软件进行数值仿真表明:文中提出的控制策略能够快速抑制电力系统的混沌状态,验证了控制方法的鲁棒性和快速性。
基金National Hi-Tech Research and Development Program of China (863 Program) Under Grant No. 2006AA04Z416Nation Natural Science Foundation of China Under Grant No. 50725828
文摘To overcome excessive computation errors and convergence failures encountered in an iterative calculation of the reliability index using the response surface method （RSM） for some nonlinear limit state functions, this study investigates an essential factor based on chaotic dynamics theory. The bifurcation diagrams of the reliability index are presented for some typical nonlinear limit state functions, and the computation results from the mapping functions due to the RSM iterations show the complicated dynamic phenomena such as the periodic oscillation, as well as bifurcation and chaos. From the numerical examples, it is concluded that the parameter of selection range fplays an important role in the convergence of the RSM iteration, and an improved RSM iterative algorithm is proposed with regard to the incorporation of the iterative sequential function of selection rangef The proposed method is shown to be efficient and to yield accurate results.
基金Project supported the National Natural Science Foundation of China (Nos. 10732020,11072008,and 11102226)the Scientific Research Foundation of Civil Aviation University of China (No. 2010QD04X)the Fundamental Research Funds for the Central Universities of China (Nos. ZXH2011D006 and ZXH2012K004)
文摘Global bifurcations and multi-pulse chaotic dynamics for a simply supported rectangular thin plate are studied by the extended Melnikov method. The rectangular thin plate is subject to transversal and in-plane excitation. A two-degree-of-freedom nonlinear nonautonomous system governing equations of motion for the rectangular thin plate is derived by the von Karman type equation and the Galerkin approach. A one-to- one internal resonance is considered. An averaged equation is obtained with a multi-scale method. After transforming the averaged equation into a standard form, the extended Melnikov method is used to show the existence of multi-pulse chaotic dynamics, which can be used to explain the mechanism of modal interactions of thin plates. A method for calculating the Melnikov function is given without an explicit analytical expression of homoclinic orbits. Furthermore, restrictions on the damping, excitation, and detuning parameters are obtained, under which the multi-pulse chaotic dynamics is expected. The results of numerical simulations are also given to indicate the existence of small amplitude multi-pulse chaotic responses for the rectangular thin plate.
基金Supported by the National Key Basic Research andDevelopment 973 Programof China (2003CB415200) and State KeyLaboratory of Water Resources and Hydropower Engineering Science(2004C011)
文摘This paper investigates synchronization within the new systems, which we denote as Liu system in this paper. New stability criteria for synchronization of linearly coupled Liu systems are attained using the Lyapunov method. Some sufficient conditions for synchronization are concluded through rigorous mathematical theory, which can be further applied to more chaotic systems. Moreover, numerical simulations are given to show the effectiveness of our synchronization criterions.
基金Project supported by the China Postdoctoral Science Foundation (Grant No 20060390318)Natural Science Foundation of Shaanxi Province (Grant No 2007F017)Fok Ying Tong Education Foundation
文摘This paper proposes an adaptive parameter identification method for breaking chaotic shift key communication from the transmitted signal in public channel. The sensitive dependence property of chaos on parameter mismatch is used for chaos adaptive synchronization and parameter identification. An index function about the synchronization error is defined and conjugate gradient method is used to minimize the index function and to search the transmitter＇s parameter （key）. By using proposed method, secure key is recovered from transmitted signal generated by low dimensional chaos and hyper chaos switching communication. Multi-parameters can also be identified from the transmitted signal with noise.
文摘This paper studies chaotic motions in quasi-integrable Hamiltonian systems with slow-varying parameters under both harmonic and noise excitations. Based on the dynamic theory and some assumptions of excited noises, an extended form of the stochastic Melnikov method is presented. Using this extended method, the homoclinic bifurcations and chaotic behavior of a nonlinear Hamiltonian system with weak feed-back control under both harmonic and Gaussian white noise excitations are analyzed in detail. It is shown that the addition of stochastic excitations can make the parameter threshold value for the occurrence of chaotic motions vary in a wider region. Therefore, chaotic motions may arise easily in the system. By the Monte-Carlo method, the numerical results for the time-history and the maximum Lyapunov exponents of an example system are finally given to illustrate that the presented method is effective.
基金Project supported by the Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education,Science and Technology(Grant No.2012-0000479)the Korea Healthcare Technology R&D Project,Ministry of Health and Welfare,Republic of Korea(Grant No.A100054)
文摘In this paper, we investigate the problem of H∞ synchronization for chaotic neural networks with time-varying delays. A new model of the networks with disturbances in both master and slave systems is presented. By constructing a suitable Lyapunov–Krasovskii functional and using a reciprocally convex approach, a novel H∞ synchronization criterion for the networks concerned is established in terms of linear matrix inequalities （LMIs） which can be easily solved by various effective optimization algorithms. Two numerical examples are given to illustrate the effectiveness of the proposed method.
基金Project supported by the National Natural Science Foundation of China(Grant No.11372102)
文摘This paper is concerned with the Hopf bifurcation control of a modified Pan-like chaotic system. Based on the Routh-Hurwtiz theory and high-dimensional Hopf bifurcation theory, the existence and stability of the Hopf bifurcation depending on selected values of the system parameters are studied. The region of the stability for the Hopf bifurcation is investigated.By the hybrid control method, a nonlinear controller is designed for changing the Hopf bifurcation point and expanding the range of the stability. Discussions show that with the change of parameters of the controller, the Hopf bifurcation emerges at an expected location with predicted properties and the range of the Hopf bifurcation stability is expanded. Finally,numerical simulation is provided to confirm the analytic results.
基金Project supported by the Natural Science Foundation of Gansu Province of China (No.ZS021-A25-007-Z)
文摘The nonlinear dynamical equations of axle symmetry are established by the method of quasi-shells for three-dimensional shallow conical single-layer lattice shells. The compatible equations are given in geometrical nonlinear range. A nonlinear differential equation containing the second and the third order nonlinear items is derived under the boundary conditions of fixed and clamped edges by the method of Galerkin. The problem of bifurcation is discussed by solving the Floquet exponent. In order to study chaotic motion, the equations of free oscillation of a kind of nonlinear dynamics system are solved. Then an exact solution to nonlinear free oscillation of the shallow conical single-layer lattice shell is found as well. The critical conditions of chaotic motion are obtained by solving Melnikov functions, some phase planes are drawn by using digital simulation proving the existence of chaotic motion.
文摘This work presents the complexity that emerges in a Bertrand duopoly between two companies in the Greek oil market, one of which is semi-public and the other is private. The game uses linear demand functions for differentiated products from the existing literature and asymmetric cost functions that arose after approaches using the published financial reports of the two oil companies (Hellenic Petroleum and Motor Oil). The game is based on the assumption of homogeneous players who are characterized by bounded rationality and follow an adjustment mechanism. The players’ decisions for each time period are expressed by two difference equations. A dynamical analysis of the game’s discrete dynamical system is made by finding the equilibrium positions and studying their stability. Numerical simulations include bifurcation diagrams and strange attractors. Lyapunov numbers’ graphs and sensitivity analysis in initial conditions prove the algebraic results and reveal the complexity and chaotic behavior of the system focusing on the two parameters k<sub>1</sub> and k<sub>2</sub> (speed of adjustment for each player). The d-Backtest method is applied through which an attempt is made to control the chaos that appears outside the stability space in order to return to the locally asymptotically stable Nash equilibrium for the system.
