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canard phenomenon in second-order autonomous unijunction transistor circuit

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Chinese Science Bulletin 1996年第17期41卷 1478-1482页

作者：徐云 Department of Electrical Engineering Tsinghua University Beijing 100084 China

In the nonlinear dynamic system the chaotic phenomenon can only appear in the autonomous system whose order is higher than three (included), which impels the research work in the nonlinear field to focus on the above-... 详细信息

关键词： nonlinear circuit canard jump.

Flight dynamics characteristics of canard rotor/wing aircraft in helicopter flight mode

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Chinese Journal of Aeronautics 2019年第7期32卷 1577-1587页

作者： Honggang GAO Ao HE Zhenghong GAO Yang NA Yangping DENG School of Aeronautics Northwestern Polytechnical University

The aerodynamic layout of the canard Rotor/Wing(CRW) aircraft in helicopter flight mode differs significantly from that of conventional helicopters. In order to study the flight dynamics characteristics of CRW aircraft in helicopter mode, first, the aerodynamic model of the main rotor system is established based on the blade element theory and wind tunnel test results. The aerodynamic forces and moments of the canard wing, horizontal tail, vertical tail and fuselage are obtained via theoretical analysis and empirical formula. The flight dynamics model of the CRW aircraft in helicopter mode is developed and validated by flight test data. Next, a method of model trimming using an optimization algorithm is proposed. The flight dynamics characteristics of the CRW are investigated by the method of linearized small perturbations via Simulink. The trim results are consistent with the conventional helicopter characteristics, and the results show that with increasing forward flight speed, the canard wing and horizontal tail can provide considerable lift,which reflects the unique characteristics of the CRW aircraft. Finally, mode analysis is implemented for the linearized CRW in helicopter mode. The results demonstrate that the stability of majority modes increases with increasing flight speed. However, one mode that diverges monotonously,and the reason is that the CRW helicopter mode has a large vertical tail compared to the conventional helicopter. The results of the dynamic analysis provide optimization guidance and reference for the overall design of the CRW aircraft in helicopter mode, and the model developed can be used for control system design.

关键词： canard rotor/wing aircraft Dynamics analysis Flight dynamics Helicopter Linearization Model building

IMPROVEMENT OF AERODYNAMIC PERFORMANCE OF SUPERSONIC AIRCRAFT USING canard SURFACE WITH TVFC

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Transactions of Nanjing University of Aeronautics and Astronautics 2006年第3期23卷 173-184页

作者： Abbas L K 陈前韩景龙南京航空航天大学航空宇航学院

The purpose of increasing the aerodynamic efficiency and enhancing the supermaneuverability for the selected supersonic aircraft is presented. Aerodynamic characteristics, the surface pressure distribution and the maximum lift are estimated for the baseline configuration for different Mach numbers and attack angles in subson- ic and supersonic potential flows, using a low-order three-dimensional panel method supported with the semi-empirical formulas of the data compendium （DATCOM）. Total nose-up and nose-down pitching moments about the center of gravity of the complete aircraft in the subsonic region depending on flight conditions and aircraft performance limitations are estimated. A software package is developed to implement the two-dimensional thrust vectoring flight control technique （pitch vectoring up and down） controlled by the advanced aerodynamic and control surface （the foreplane or the canard）. Results show that the canard with the thrust vectoring produces enough nose-down moment and can support the stabilizer at high maneuvers. The suggested surface can increase the aerodynamic efficiency （lift-to-drag ratio） of the baseline configuration by 5%-6% in subsonic and supersonic flight regimes.

关键词： aerodynamic efficiency maneuverability canard thrust vectoring flight control (TVFC)

Existence of canards under Non-generic Conditions

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Chinese Annals of Mathematics,Series B 2009年第3期30卷 239-250页

作者： Feng XIE Maoan HAN Department of Applied Mathematics Donghua University Shanghai 201620 China Division of Computational Science E-Institute of Shanghai Universities Shanghai Jiao Tong University Shanghai 200030China Department of Mathematics Shanghai Normal University Shanghai 200234 China

The canard phenomenon occurring in planar fast-slow systems under non-generic conditions is *** the critical manifold has a non-generic fold point,by using the method of asymptotic analysis combined with the recently developed blow-up technique,the existence of a canard is established and the asymptotic expansion of the parameter for which a canard exists is obtained.

关键词： canard Slow manifold Singular perturbation Blow-up Non-genericcondition

Nonlinear and Stochastic Dynamics of Coupled FitzHugh-Nagumo Neurons

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Nonlinear and Stochastic Dynamics of Coupled FitzHugh-Nagumo...

作者：李秀敏天津大学

学位级别：硕士

近年来,非线性动力学在神经科学中受到了广泛的关注。本文主要研究耦合FHN神经元模型的一种复杂非线性动力学,即canard现象和随机动力学。canard解一般存在于具有二维临界流形(慢流形)的三维奇异摄动系统中。这类解经过慢流形的稳定支... 详细信息

近年来,非线性动力学在神经科学中受到了广泛的关注。本文主要研究耦合FHN神经元模型的一种复杂非线性动力学,即canard现象和随机动力学。canard解一般存在于具有二维临界流形(慢流形)的三维奇异摄动系统中。这类解经过慢流形的稳定支流后会一反常态沿着不稳定支流演化一段时间。参数位于canard区域的神经元模型可表现出非常复杂的动力学行为并对外界干扰十分敏感。这一特性对于生物系统的微弱信号传输很有意义,并为其实现低能损耗提供了条件。首先,本文从理论分析和数值仿真的角度证明了canard在化学耦合FHN神经元模型中的存在性,并分析了各参数对canard分岔的影响。一般认为,三维系统中的canard对于小参数变化具有鲁棒性[1;2],但在此系统中canard敏感依赖于外部输入电流而只存在与其很小的参数区域内。其次,本文研究了三个耦合神经元的随机动力学特性,将两种不同的耦合形式——化学突触耦合与线性电耦合对系统的相干共振(CR)和随机共振(SR)进行对比。在这两种情况中,当噪音强度达到某一中间值时神经元都可表现出最优的CR和SR,即最优的信号传递。但通过比较我们发现,对于局部的微小输入信号,化学突触耦合神经元所表现出的CR和SR都明显优于线性电耦合的神经元。另外,当神经元参数位于或接近canard区域时,此两种随机动力学特性达到最优。最后,本文还分析了细胞个体差异性和噪音时空独立性对信号传递的影响。同文献[3]中的结论一致,这两种因素都能够加强信息的传输。这是由于不同的个体以及不同的噪音来源都增加了系统的多样性从而加强了个体之间的竞争,此现象普遍存在于实际的生物系统中。

关键词： FHN神经元 canard 分岔化学突触耦合相干共振随机共振

Aerodynamic Design for Three-Dimensional Multi-lifting Surfaces at Transonic Flow

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Chinese Journal of Aeronautics 2006年第1期19卷 24-30页

作者：杨青真张仲寅 Thomas Streit Georg Wichmann 郑勇 School of Dynamics and Energy Northwestern Polytechnical University Xi'an 71002 China School of Aeronautics Northwestern Polytechnical University Xi'an 71002 China Institute of Aerodynamics and Flow Technology German Aerospace Center(DLR) Braunschweig 38108 Germany

An aerodynamic design method and corresponding codes are developed for three-dimensional multi lifting surfaces at transonic flow. It is based on the ＂iterative residual correction＂ concept that is successfully used for transonic wing design and subsonic multi-lifting surface design. The up-wind scheme is introduced into governing equations of multi-lifting surface design method and automatically acted when supersonic flow appears on the surface. A series of interface codes are programmed, including a target-pressure modification tool. Using the improved inverse aerodynamic design code, TAU code and interface codes, the transonic multi-lifting aerodynamic design software system is founded. Two cases of canard-wing configuration have been performed to validate the method and codes. The results show that the convergence of analysis/design iteration is very good at higher speed transonic flow.

关键词： aerodynamic design transonic flow iterative residual correction multi-liftlng surfaces canard wing

Critical Dynamics of a Nonlinear Second Order Autonomous System

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Tsinghua Science and Technology 1997年第3期2卷 40-43,61页

作者：徐云

The critical dynamic behavior of a nonlinear second order autonomous circuit is presented. In the vicinities of the critical points of the control parameters of various types of canard limiting cycles appearing in the circuit, according to the threshold values selected an unstable state occurs between the threshold values of the control parameters. 

关键词： nonlinear circuit critical point canard