In the paper, a novel four-wing hyper-chaotic system is proposed and analyzed. A rare dynamic phenomenon is found that this new system with one equilibrium generates a four-wing-hyper-chaotic attractor as parameter va...In the paper, a novel four-wing hyper-chaotic system is proposed and analyzed. A rare dynamic phenomenon is found that this new system with one equilibrium generates a four-wing-hyper-chaotic attractor as parameter varies. The system has rich and complex dynamical behaviors, and it is investigated in terms of Lyapunov exponents, bifurcation diagrams, Poincare maps, frequency spectrum, and numerical simulations. In addition, the theoretical analysis shows that the system undergoes a Hopf bifurcation as one parameter varies, which is illustrated by the numerical simulation. Finally, an analog circuit is designed to implement this hyper-chaotic system.展开更多
This paper presents a new 3D quadratic autonomous chaotic system which contains five system parameters and three quadratic cross-product terms,and the system can generate a single four-wing chaotic attractor with wide...This paper presents a new 3D quadratic autonomous chaotic system which contains five system parameters and three quadratic cross-product terms,and the system can generate a single four-wing chaotic attractor with wide parameter ranges. Through theoretical analysis,the Hopf bifurcation processes are proved to arise at certain equilibrium points.Numerical bifurcation analysis shows that the system has many interesting complex dynamical behaviours;the system trajectory can evolve to a chaotic attractor from a periodic orbit or a fixed point as the proper parameter varies. Finally,an analog electronic circuit is designed to physically realize the chaotic system;the existence of four-wing chaotic attractor is verified by the analog circuit realization.展开更多
Sliding mode control is an important method used in nonlinear control systems. In robust control systems, the sliding mode control is often adopted due to its inherent advantages of easy realization, fast response and...Sliding mode control is an important method used in nonlinear control systems. In robust control systems, the sliding mode control is often adopted due to its inherent advantages of easy realization, fast response and good transient performance as well as its insensitivity to parameter uncertainties and disturbances. In this paper, we derive new results based on the sliding mode control for the anti-synchronization of identical Qi three-dimensional (3D) four-wing chaotic systems (2008) and identical Liu 3D four-wing chaotic systems (2009). The stability results for the anti-synchronization schemes derived in this paper using sliding mode control (SMC) are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the SMC method is very effective and convenient to achieve global chaos anti-synchronization of the identical Qi four-wing chaotic systems and identical Liu four-wing chaotic systems. Numerical simulations are shown to illustrate and validate the synchronization schemes derived in this paper.展开更多
In this paper,some basic properties of a new four-dimensional(4 D)continuous autonomous chaotic system,in which each equation contains a cubic cross-product term,are further analyzed.The new system has 9 equilibria di...In this paper,some basic properties of a new four-dimensional(4 D)continuous autonomous chaotic system,in which each equation contains a cubic cross-product term,are further analyzed.The new system has 9 equilibria displaying graceful symmetry with respect to the origin and coordinate planes,and the stability of them are discussed.Then detailed bifurcation analysis is given to demonstrate the evolution processes of the system.Numerical simulations show that the system evolves chaotic motions through period-doubling bifurcation or intermittence chaos while the system parameters vary.We design a new scheme of generalized projective synchronization,so-called unified generalized projective synchronization,whose response signal synchronizes with the linear combination of drive signal.The design has the advantages of containing complete synchronization,anti-synchronization and disorder synchronization over the usual generalized projective synchronization,such that it can provide greater security in secure communication.Based on Lyapunov stability theorem,some sufficient conditions for the new synchronization are inferred.Numerical simulations demonstrate the effectiveness and feasibility of the method by employing the four-wing chaotic system.展开更多
Recently,a novel concept of flapping Micro-Air-Vehicles(FMAVs)with four wings has been proposed,which potentially utilizes the clap-and-fling effect for lift enhancement and agile maneuvers through an adjustment of wi...Recently,a novel concept of flapping Micro-Air-Vehicles(FMAVs)with four wings has been proposed,which potentially utilizes the clap-and-fling effect for lift enhancement and agile maneuvers through an adjustment of wing kinematics.However,the application of the clap-and-fling effect in the four-winged FMAVs is underexplored and the dynamic stability is still unclear.In this paper,aerodynamics and flight dynamic stability of the four-winged FMAVs are studied experimentally and numerically.Results show that the clap-and-fling effect is observed when the flapping frequency is above 18 Hz.Due to the clap-and-fling effect,the lift generation and aerodynamic efficiency are both improved,which is mainly attributed to the fling phase.Further studies show that the clap-and-fling effect becomes weaker as the wing root spacing increases and is almost absent at a wing root spacing of 1.73 chord length.In addition,a wing with an aspect ratio of 3 can increase both lift generation and efficiency due to the clap-and-fling effect.Finally,according to the dynamic stability analysis of the four-winged FMAV,the divergence speed of the lateral oscillation mode is about 4 times faster than that of the longitudinal oscillation mode.Our results can provide guidance on the design and control of four-winged FMAVs.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.10772135 and 60874028)the Young Scientists Fund of the National Natural Science Foundation of China(Grant No.11202148)+2 种基金the Incentive Funding of the National Research Foundation of South Africa(GrantNo.IFR2009090800049)the Eskom Tertiary Education Support Programme of South Africathe Research Foundation of Tianjin University of Science and Technology
文摘In the paper, a novel four-wing hyper-chaotic system is proposed and analyzed. A rare dynamic phenomenon is found that this new system with one equilibrium generates a four-wing-hyper-chaotic attractor as parameter varies. The system has rich and complex dynamical behaviors, and it is investigated in terms of Lyapunov exponents, bifurcation diagrams, Poincare maps, frequency spectrum, and numerical simulations. In addition, the theoretical analysis shows that the system undergoes a Hopf bifurcation as one parameter varies, which is illustrated by the numerical simulation. Finally, an analog circuit is designed to implement this hyper-chaotic system.
基金Project supported by the National Natural Science Foundation of China(Grant Nos 60774088 and 10772135)the Foundation of the Application Base and Frontier Technology Research Project of Tianjin,China (Grant Nos 07JCZDJC09600,08JCZDJC21900 and 08JCZDJC18600)the Tianjin Key Laboratory for Control Theory & Applications in Complicated Industry Systems of China
文摘This paper presents a new 3D quadratic autonomous chaotic system which contains five system parameters and three quadratic cross-product terms,and the system can generate a single four-wing chaotic attractor with wide parameter ranges. Through theoretical analysis,the Hopf bifurcation processes are proved to arise at certain equilibrium points.Numerical bifurcation analysis shows that the system has many interesting complex dynamical behaviours;the system trajectory can evolve to a chaotic attractor from a periodic orbit or a fixed point as the proper parameter varies. Finally,an analog electronic circuit is designed to physically realize the chaotic system;the existence of four-wing chaotic attractor is verified by the analog circuit realization.
文摘Sliding mode control is an important method used in nonlinear control systems. In robust control systems, the sliding mode control is often adopted due to its inherent advantages of easy realization, fast response and good transient performance as well as its insensitivity to parameter uncertainties and disturbances. In this paper, we derive new results based on the sliding mode control for the anti-synchronization of identical Qi three-dimensional (3D) four-wing chaotic systems (2008) and identical Liu 3D four-wing chaotic systems (2009). The stability results for the anti-synchronization schemes derived in this paper using sliding mode control (SMC) are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the SMC method is very effective and convenient to achieve global chaos anti-synchronization of the identical Qi four-wing chaotic systems and identical Liu four-wing chaotic systems. Numerical simulations are shown to illustrate and validate the synchronization schemes derived in this paper.
基金Supported by the National Natural Science Foundation of China(61863022)the Natural Science Foundation of Gansu Province(17JR5RA096)。
文摘In this paper,some basic properties of a new four-dimensional(4 D)continuous autonomous chaotic system,in which each equation contains a cubic cross-product term,are further analyzed.The new system has 9 equilibria displaying graceful symmetry with respect to the origin and coordinate planes,and the stability of them are discussed.Then detailed bifurcation analysis is given to demonstrate the evolution processes of the system.Numerical simulations show that the system evolves chaotic motions through period-doubling bifurcation or intermittence chaos while the system parameters vary.We design a new scheme of generalized projective synchronization,so-called unified generalized projective synchronization,whose response signal synchronizes with the linear combination of drive signal.The design has the advantages of containing complete synchronization,anti-synchronization and disorder synchronization over the usual generalized projective synchronization,such that it can provide greater security in secure communication.Based on Lyapunov stability theorem,some sufficient conditions for the new synchronization are inferred.Numerical simulations demonstrate the effectiveness and feasibility of the method by employing the four-wing chaotic system.
基金National Natural Science Foundation of China(NSFC,No.11672022 and No.11902017).
文摘Recently,a novel concept of flapping Micro-Air-Vehicles(FMAVs)with four wings has been proposed,which potentially utilizes the clap-and-fling effect for lift enhancement and agile maneuvers through an adjustment of wing kinematics.However,the application of the clap-and-fling effect in the four-winged FMAVs is underexplored and the dynamic stability is still unclear.In this paper,aerodynamics and flight dynamic stability of the four-winged FMAVs are studied experimentally and numerically.Results show that the clap-and-fling effect is observed when the flapping frequency is above 18 Hz.Due to the clap-and-fling effect,the lift generation and aerodynamic efficiency are both improved,which is mainly attributed to the fling phase.Further studies show that the clap-and-fling effect becomes weaker as the wing root spacing increases and is almost absent at a wing root spacing of 1.73 chord length.In addition,a wing with an aspect ratio of 3 can increase both lift generation and efficiency due to the clap-and-fling effect.Finally,according to the dynamic stability analysis of the four-winged FMAV,the divergence speed of the lateral oscillation mode is about 4 times faster than that of the longitudinal oscillation mode.Our results can provide guidance on the design and control of four-winged FMAVs.
