A typical airfoil section system with freeplay is investigated in the paper. The classic quasi-steady flow model is applied to calculate the aerodynamics, and a piecewise-stiffness model is adopted to characterize the...A typical airfoil section system with freeplay is investigated in the paper. The classic quasi-steady flow model is applied to calculate the aerodynamics, and a piecewise-stiffness model is adopted to characterize the non- linearity of the airfoil section＇s freeplay. There are two crit- ical speeds in the system, i.e., a lower critical speed, above which the system might generate limit cycle oscillation, and an upper critical one, above which the system will flutter. Then a Poincar6 map is constructed for the limit cycle os- cillations by using piecewise-linear solutions with and with- out contact in the system. Through analysis of the Poincar6 map, a series of equations which can determine the frequen- cies of period-1 limit cycle oscillations at any flight veloc- ity are derived. Finally, these analytic results are compared to the results of numerical simulations, and a good agree- ment is found. The effects of freeplay value and contact stiffness ratio on the limit cycle oscillation are also analyzed through numerical simulations of the original system. More- over, there exist multi-periods limit cycle oscillations and even complicated ＂chaotic＂ oscillations may occur, which are usually found in smooth nonlinear dynamic systems.展开更多
We present a fractional-order three-dimensional chaotic system, which can generate four-wing chaotic attractor. Dy- namics of the fractional-order system is investigated by numerical simulations. To rigorously verify ...We present a fractional-order three-dimensional chaotic system, which can generate four-wing chaotic attractor. Dy- namics of the fractional-order system is investigated by numerical simulations. To rigorously verify the chaos properties of this system, the existence of horseshoe in the four-wing attractor is presented. Firstly, a Poincar6 section is selected properly, and a first-return Poincar6 map is established. Then, a one-dimensional tensile horseshoe is discovered, which verifies the chaos existence of the system in mathematical view. Finally, the fractional-order chaotic attractor is imple- mented physically with a field-programmable gate array （FPGA） chip, which is useful in further engineering applications of information encryption and secure communications.展开更多
The existence of Smale horseshoes for a certain discretized perturbed nonlinear Schroedinger （NLS） equations was established by using n-dimensional versions of the Conley-Moser conditions. As a result, the discretiz...The existence of Smale horseshoes for a certain discretized perturbed nonlinear Schroedinger （NLS） equations was established by using n-dimensional versions of the Conley-Moser conditions. As a result, the discretized perturbed NLS system is shown to possess an invadant set A on which the dynamics is topologically conjugate to a shift on four symbols.展开更多
The aim of this paper is to contribute to the identification and characterization of the various types of intuition put forward by Poincar6, taking his texts as a laboratory for looking for what intuition might be. I ...The aim of this paper is to contribute to the identification and characterization of the various types of intuition put forward by Poincar6, taking his texts as a laboratory for looking for what intuition might be. I will stress that these diverse conceptions are mainly formulated in the context of Poincar6＇s controversies in opposition to logicism, to formalism, and in the context of Poincar6＇s very peculiar conventionalism. I will try to demonstrate that, in each case, Poincar~ comes close to a specific tradition （Kant, of course, but also Leibniz and Peirce）.展开更多
We study the collective dynamics of a non-dissipative two-coupled pendulum system, including phase synchronization （PS） and measure synchronization （MS）. We find that as the coupling intensity between the two pend...We study the collective dynamics of a non-dissipative two-coupled pendulum system, including phase synchronization （PS） and measure synchronization （MS）. We find that as the coupling intensity between the two pendulums increases, the PS happens prior to the MS. We also present a three-dimensional phase space representation of MS, from which a more detailed information about evolution can be obtained. Fu~.hermore, the order parameters are introduced to describe the phase transition between PS and MS. Finally, through the analysis of the Poincar6 sections, we show that the system exhibits separatrix crossing behavior right at the MS transition point, and as the total initial energy increases, the Hamiltonian chaos will arise with separatrix chaos at the chaotic MS transition point.展开更多
An oscillator with dry friction under external excitation is considered. The Poincar@ map can be established according to the series solution near equilibrium in the case of 1：4 resonance. Based on the theory of norm...An oscillator with dry friction under external excitation is considered. The Poincar@ map can be established according to the series solution near equilibrium in the case of 1：4 resonance. Based on the theory of normal forms, the map is reduced into its normal form. It is shown that the Neimark-Sacker （N-S） bifurcations may occour. The theoretical results are verified with the numerical simulations.展开更多
We show that in a Q-doubling space （X, d, μ）, Q 〉 1, which satisfies a chain condition, if we have a Q-Poincare inequality for a pair of functions （u, g） where g ∈ LQ（X）, then u has Lebesgue points 7-th-a.e. ...We show that in a Q-doubling space （X, d, μ）, Q 〉 1, which satisfies a chain condition, if we have a Q-Poincare inequality for a pair of functions （u, g） where g ∈ LQ（X）, then u has Lebesgue points 7-th-a.e. for h（t） = log1-Q-c（1/t）. We also discuss how the existence of Lebesgue points follows for u ∈ W1,Q（x） where （X, d, μ） is a complete Q-doubling space supporting a Q-Poincar; inequality for Q 〉 1.展开更多
基金supported by the National Science Fund for Distinguished Young Scholars in China(11225212)the Young Teachers' Funds of Hunan Province,China
文摘A typical airfoil section system with freeplay is investigated in the paper. The classic quasi-steady flow model is applied to calculate the aerodynamics, and a piecewise-stiffness model is adopted to characterize the non- linearity of the airfoil section＇s freeplay. There are two crit- ical speeds in the system, i.e., a lower critical speed, above which the system might generate limit cycle oscillation, and an upper critical one, above which the system will flutter. Then a Poincar6 map is constructed for the limit cycle os- cillations by using piecewise-linear solutions with and with- out contact in the system. Through analysis of the Poincar6 map, a series of equations which can determine the frequen- cies of period-1 limit cycle oscillations at any flight veloc- ity are derived. Finally, these analytic results are compared to the results of numerical simulations, and a good agree- ment is found. The effects of freeplay value and contact stiffness ratio on the limit cycle oscillation are also analyzed through numerical simulations of the original system. More- over, there exist multi-periods limit cycle oscillations and even complicated ＂chaotic＂ oscillations may occur, which are usually found in smooth nonlinear dynamic systems.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61502340 and 61374169)the Application Base and Frontier Technology Research Project of Tianjin,China(Grant No.15JCYBJC51800)the South African National Research Foundation Incentive Grants(Grant No.81705)
文摘We present a fractional-order three-dimensional chaotic system, which can generate four-wing chaotic attractor. Dy- namics of the fractional-order system is investigated by numerical simulations. To rigorously verify the chaos properties of this system, the existence of horseshoe in the four-wing attractor is presented. Firstly, a Poincar6 section is selected properly, and a first-return Poincar6 map is established. Then, a one-dimensional tensile horseshoe is discovered, which verifies the chaos existence of the system in mathematical view. Finally, the fractional-order chaotic attractor is imple- mented physically with a field-programmable gate array （FPGA） chip, which is useful in further engineering applications of information encryption and secure communications.
文摘The existence of Smale horseshoes for a certain discretized perturbed nonlinear Schroedinger （NLS） equations was established by using n-dimensional versions of the Conley-Moser conditions. As a result, the discretized perturbed NLS system is shown to possess an invadant set A on which the dynamics is topologically conjugate to a shift on four symbols.
文摘The aim of this paper is to contribute to the identification and characterization of the various types of intuition put forward by Poincar6, taking his texts as a laboratory for looking for what intuition might be. I will stress that these diverse conceptions are mainly formulated in the context of Poincar6＇s controversies in opposition to logicism, to formalism, and in the context of Poincar6＇s very peculiar conventionalism. I will try to demonstrate that, in each case, Poincar~ comes close to a specific tradition （Kant, of course, but also Leibniz and Peirce）.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11104217,11174165,and 11275099)
文摘We study the collective dynamics of a non-dissipative two-coupled pendulum system, including phase synchronization （PS） and measure synchronization （MS）. We find that as the coupling intensity between the two pendulums increases, the PS happens prior to the MS. We also present a three-dimensional phase space representation of MS, from which a more detailed information about evolution can be obtained. Fu~.hermore, the order parameters are introduced to describe the phase transition between PS and MS. Finally, through the analysis of the Poincar6 sections, we show that the system exhibits separatrix crossing behavior right at the MS transition point, and as the total initial energy increases, the Hamiltonian chaos will arise with separatrix chaos at the chaotic MS transition point.
基金Project supported by the National Natural Science Foundation of China(No.11172246)the Fundamental Research Funds for the Central Universities of China(No.SWJTU11ZT15)
文摘An oscillator with dry friction under external excitation is considered. The Poincar@ map can be established according to the series solution near equilibrium in the case of 1：4 resonance. Based on the theory of normal forms, the map is reduced into its normal form. It is shown that the Neimark-Sacker （N-S） bifurcations may occour. The theoretical results are verified with the numerical simulations.
基金supported by the Academy of Finland via the Centre of Excellence in Analysis and Dynamics Research(Grant No.271983)
文摘We show that in a Q-doubling space （X, d, μ）, Q 〉 1, which satisfies a chain condition, if we have a Q-Poincare inequality for a pair of functions （u, g） where g ∈ LQ（X）, then u has Lebesgue points 7-th-a.e. for h（t） = log1-Q-c（1/t）. We also discuss how the existence of Lebesgue points follows for u ∈ W1,Q（x） where （X, d, μ） is a complete Q-doubling space supporting a Q-Poincar; inequality for Q 〉 1.
