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 Poincare-Bertrand formula takes an important position in the study of complex singular integral. The Poincare-Bertrand formula on the complex sphere in the multidimensional complex Euclidian spaces was given by Sh...The Poincare-Bertrand formula takes an important position in the study of complex singular integral. The Poincare-Bertrand formula on the complex sphere in the multidimensional complex Euclidian spaces was given by Sheng Gong. Using the method of solid angular coefficient, the authors extend the Poincare-Bertrand formula on the complex sphere to the building domain of the complex biballs, and obtain a more general Poincare- Bertrand formula with the solid angular coefficients.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
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
基金Supported by the National Natural Science Foundation of China(71403069)the 51th of the Postdoctoral Science Foundation of China(AUGA4130916512)Introduction of Hainan Medical University Scientific Research Grants Project
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 Poincare-Bertrand formula takes an important position in the study of complex singular integral. The Poincare-Bertrand formula on the complex sphere in the multidimensional complex Euclidian spaces was given by Sheng Gong. Using the method of solid angular coefficient, the authors extend the Poincare-Bertrand formula on the complex sphere to the building domain of the complex biballs, and obtain a more general Poincare- Bertrand formula with the solid angular coefficients.
基金Supported by Chinese National Science Foundation(Grant Nos.11226278 and 11201484)the Fundamental Research Funds for the Central Universities(14CX02009A)
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.
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.
