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Hyper Catastrophe on 4-Dimensional Canards
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作者 Kiyoyuki Tchizawa Shuya Kanagawa 《Advances in Pure Mathematics》 2024年第4期196-203,共8页
When discovering the potential of canards flying in 4-dimensional slow-fast system with a bifurcation parameter, the key notion “symmetry” plays an important role. It is of one parameter on slow vector field. Then, ... When discovering the potential of canards flying in 4-dimensional slow-fast system with a bifurcation parameter, the key notion “symmetry” plays an important role. It is of one parameter on slow vector field. Then, it should be determined to introduce parameters to all slow/fast vectors. It is, however, there might be no way to explore for another potential in this system, because the geometrical structure is quite different from the system with one parameter. Even in this system, the “symmetry” is also useful to obtain the potentials classified by R. Thom. In this paper, via the coordinates changing, the possible way to explore for the potential will be shown. As it is analyzed on “hyper finite time line”, or done by using “non-standard analysis”, it is called “Hyper Catastrophe”. In the slow-fast system which includes a very small parameter , it is difficult to do precise analysis. Thus, it is useful to get the orbits as a singular limit. When trying to do simulations, it is also faced with difficulty due to singularity. Using very small time intervals corresponding small , we shall overcome the difficulty, because the difference equation on the small time interval adopts the standard differential equation. These small intervals are defined on hyper finite number N, which is nonstandard. As and the intervals are linked to use 1/N, the simulation should be done exactly. 展开更多
关键词 canards Flying 4-Dimensional Slow-Fast System Hyper Catastrophe
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Canards Flying on Bifurcation
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作者 Shuya Kanagawa Kiyoyuki Tchizawa 《Advances in Pure Mathematics》 2023年第6期412-424,共13页
There exists a property “structural stability” for “4-dimensional canards” which is a singular-limit solution in a slow-fast system with a bifurcation parameter. It means that the system includes the possibility t... There exists a property “structural stability” for “4-dimensional canards” which is a singular-limit solution in a slow-fast system with a bifurcation parameter. It means that the system includes the possibility to have some critical values on the bifurcation parameter. Corresponding to these values, the pseudo-singular point, which is a singular point in the time-scaled-reduced system should be changed to another one. Then, the canards may fly to another pseudo-singular point, if possible. Can the canards fly? The structural stability gives the possibility for the canards flying. The precise reasons why happen are described in this paper. 展开更多
关键词 Canard Solution Slow-Fast System Nonstandard Analysis Hilbert’s 16th Problem Brownian Motion Stochastic Differential Equation
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Influence of control strategy on stability of dual-spin projectiles with fixed canards 被引量:7
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作者 Yu Wang Xiao-ming Wang Ji-yan Yu 《Defence Technology(防务技术)》 SCIE EI CAS CSCD 2018年第6期709-719,共11页
Existing literature has shown that the control force at the nose could cause dynamic instability for controlled projectiles. To lower the adverse impact on the dual-spin projectile with fixed canards under the premise... Existing literature has shown that the control force at the nose could cause dynamic instability for controlled projectiles. To lower the adverse impact on the dual-spin projectile with fixed canards under the premise of meeting guidance system requirements, the influence of control moment provided by a motor on the flight stability is analyzed in this paper. Firstly, the effect of the rolling movement on stability is analyzed based on the stability criterion derived using the Hurwitz stability theory. Secondly, the evaluation parameters combining the features of different control periods that could assess the variation of stability features after the motor torque are obtained. These effective formulas are used to indicate that, to reduce the flight instability risks, the stabilized rolling speed of roll speed keeping period should be as small as possible; the variation trend of motor torque during the rolling speed controlling period and the roll angle of the forward body during roll angle switching period are recommended corresponding to the projectile and trajectory characteristics. Moreover,detailed numerical simulations of 155 mm dual-spin projectile are satisfactory agreement with the theoretical results. 展开更多
关键词 Dual-spin PROJECTILE Fixed canards Control strategy Flight STABILITY
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Canards in a rheodynamic model of cardiac pressure pulsations
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作者 谢峰 陈贤峰 《Chinese Physics B》 SCIE EI CAS CSCD 2007年第9期2635-2639,共5页
This paper reports on the canard phenomenon occurring in a rheodynamic model of cardiac pressure pulsations. By singular perturbation techniques the corresponding parameter value at which canards exist is obtained. Th... This paper reports on the canard phenomenon occurring in a rheodynamic model of cardiac pressure pulsations. By singular perturbation techniques the corresponding parameter value at which canards exist is obtained. The physiological significance of canards in this model is given. 展开更多
关键词 canards rheodynamic model cardiac self-oscillations singular perturbations
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Structural Stability in 4-Dimensional Canards
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作者 Shuya Kanagawa Kiyoyuki Tchizawa 《Advances in Pure Mathematics》 2022年第11期600-613,共14页
Let us consider higher dimensional canards in a sow-fast system R<sup>2+2</sup> with a bifurcation parameter. Then, the slow manifold sometimes shows various aspects due to the bifurcation. Introducing a k... Let us consider higher dimensional canards in a sow-fast system R<sup>2+2</sup> with a bifurcation parameter. Then, the slow manifold sometimes shows various aspects due to the bifurcation. Introducing a key notion “symmetry” to the slow-fast system, it becomes clear when the pseudo singular point obtains the structural stability or not. It should be treated with a general case. Then, it will also be given about the sufficient conditions for the existence of the center manifold under being “symmetry”. The higher dimensional canards in the sow-fast system are deeply related to Hilbert’s 16th problem. Furthermore, computer simulations are done for the systems having Brownian motions. As a result, the rigidity for the system is confirmed. 展开更多
关键词 Canard Solution Slow-Fast System Nonstandard Analysis Hilbert’s 16th Problem Brownian Motion Stochastic Differential Equation
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Impact point prediction guidance based on iterative process for dual-spin projectile with fixed canards 被引量:5
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作者 Xin ZHANG Xiaoxian YAO Qiushi ZHENG 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2019年第8期1967-1981,共15页
The fixed canards configuration of a dual-spin projectile makes it difficult to apply the traditional guidance law. In this study, a modified impact point prediction guidance strategy based on an iterative process was... The fixed canards configuration of a dual-spin projectile makes it difficult to apply the traditional guidance law. In this study, a modified impact point prediction guidance strategy based on an iterative process was developed for a class of dual-spin projectiles with fixed canards, to reduce the impact point dispersion. The guidance strategy is dependent on the modified projectile linear theory to rapidly predict the flight states and the impact point. For projectiles with control applied to the trajectory, the modified projectile linear theory method is known to achieve poor impact point prediction. To improve the prediction accuracy, improvements were made to the modified projectile linear theory by considering the products of the yaw rate and other small quantities.The guidance strategy is based on the iterative process for the continuous adjustment of the expected output of the roll angle of the course correction fuze, to minimize the direction error between the predicted impact point and target location. Studies were conducted on a model dual-spin projectile configuration to demonstrate the guidance details. The numerical simulations indicate that the proposed guidance strategy can effectively reduce the projectile impact point dispersion. 展开更多
关键词 Dual-spin PROJECTILE withfixed canards GUIDANCE strategy Linear theory PROJECTILE characteristics Trajectory PREDICTION
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Existence of Canards under Non-generic Conditions 被引量:1
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作者 Feng XIE Maoan HAN 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2009年第3期239-250,共12页
The canard phenomenon occurring in planar fast-slow systems under non-generic conditions is investigated.When the critical manifold has a non-generic fold point,by using the method of asymptotic analysis combined with... The canard phenomenon occurring in planar fast-slow systems under non-generic conditions is investigated.When 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. 展开更多
关键词 CANARD Slow manifold Singular perturbation BLOW-UP Non-genericcondition
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A review of dual-spin projectile stability 被引量:3
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作者 James Norris Amer Hameed +1 位作者 John Economou Simon Parker 《Defence Technology(防务技术)》 SCIE EI CAS CSCD 2020年第1期1-9,共9页
This paper gives a succinct review of dual-spinprojectile stability and some technologies relating to them.It describes how the traditional stability factors from linear projectile theory are modified to better descri... This paper gives a succinct review of dual-spinprojectile stability and some technologies relating to them.It describes how the traditional stability factors from linear projectile theory are modified to better describe a controlled dual-spin projectile.Finally,it reviews works which have investigated how different aspects of a controlled dual-spin design can affect flight stability,primarily airframe structure and canard properties.A conclusion is given,highlighting important guidelines from the enclosed discussions. 展开更多
关键词 Guided PROJECTILES Dual-spin Gyroscopic Dynamic STABILITY canards
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On Canard Homoclinic of a Liénard Perturbation System
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作者 Makoto Hayashi 《Applied Mathematics》 2011年第10期1221-1224,共4页
The classification on the orbits of some Liénard perturbation system with several parameters, which is relation to the example in [1] or [2], is discussed. The conditions for the parameters in order that the syst... The classification on the orbits of some Liénard perturbation system with several parameters, which is relation to the example in [1] or [2], is discussed. The conditions for the parameters in order that the system has a unique limit cycle, homoclinic orbits, canards or the unique equilibrium point is globally asymptotic stable are given. The methods in our previous papers are used for the proofs. 展开更多
关键词 Liénard SYSTEM canards Limit Cycles HOMOCLINIC ORBITS Global ASYMPTOTIC Stability
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IMPROVEMENT OF AERODYNAMIC PERFORMANCE OF SUPERSONIC AIRCRAFT USING CANARD SURFACE WITH TVFC
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作者 Abbas L K 陈前 韩景龙 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 2006年第3期173-184,共12页
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 max... 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. 展开更多
关键词 aerodynamic efficiency MANEUVERABILITY CANARD thrust vectoring flight control (TVFC)
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Aerodynamic Design for Three-Dimensional Multi-lifting Surfaces at Transonic Flow 被引量:2
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作者 杨青真 张仲寅 +2 位作者 Thomas Streit Georg Wichmann 郑勇 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2006年第1期24-30,共7页
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... 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. 展开更多
关键词 aerodynamic design transonic flow iterative residual correction multi-liftlng surfaces CANARD WING
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Rolling Control Characteristic Experimental Investigation of a Canard Missile with Free-Spinning Tail 被引量:1
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作者 雷娟棉 吴甲生 孟令涛 《Journal of Beijing Institute of Technology》 EI CAS 2006年第1期36-38,共3页
To study the rolling control characteristics of a canard-controlled missile, a series of wind tunnel experiment is conducted. The experimental method, the structure features of wind tunnel model and the experimental r... To study the rolling control characteristics of a canard-controlled missile, a series of wind tunnel experiment is conducted. The experimental method, the structure features of wind tunnel model and the experimental results are introduced in this paper. The experimental data show that the canard is an inefficient rolling control device for canard-controlled missile with fixed tail fins; but for the free-spinning tail fin configuration, the canard can conduct rolling control of the missile, and even have higher controlling efficiency under larger canard deflection angle. 展开更多
关键词 canard missile aerodynamic characteristics wind tunnel experiment free-spinning tail rolling control characteristics
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A Calculation Method of Rolling Characteristics of Canard Missile with Free-Spinning Tails 被引量:1
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作者 Ping’an Liu Mingyuan Liu 《Journal of Harbin Institute of Technology(New Series)》 EI CAS 2019年第6期62-68,共7页
The steady flow field of a canard missile on different angles of attack and Mach numbers were studied. Based on analysis, a method was proposed to reduce the calculation for the rolling characteristics of the canard m... The steady flow field of a canard missile on different angles of attack and Mach numbers were studied. Based on analysis, a method was proposed to reduce the calculation for the rolling characteristics of the canard missile with free-spinning tails, and was tested to obtain the relations between rolling moment coefficient, Mach number, and angle of attack. All the computed rolling moment coefficients obtained from the proposed method greatly agreed with the experimental results of FD-06 wind tunnel in CAAA, which proved that the method can not only reduce the calculation cost but also keep precision in calculating the rolling characteristics of canard missiles. 展开更多
关键词 numerical simulation canard missile free-spinning tail wind tunnel test rolling characteristics
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THE CANARD-WING INTERFERENCE AND STALL SAFETY OF LIGHT CANARD AIRCRAFT
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作者 Bai Zhenzhu Xie Xiaobin Nanjing Aeronautical Institute Nanjing 210016, P.R.C 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 1991年第2期226-234,共9页
In this article, the interference between canard and wing is discussed on the basis of wind-tunnel test, with a brief review of the development of aerodynamic configurations of AD-100 / 200 (two light canard aircraft ... In this article, the interference between canard and wing is discussed on the basis of wind-tunnel test, with a brief review of the development of aerodynamic configurations of AD-100 / 200 (two light canard aircraft designed by NAI) .The safety against stall of a canard is also discussed based upon flight test.The rule 'canard stall first'is introduced as an effective measure to improve safety against stall. It has been pointed out that the rule may threaten the flight safety at low-altitude. Finally,what a designer can do to remove the threat is presented. 展开更多
关键词 In than THE CANARD-WING INTERFERENCE AND STALL SAFETY OF LIGHT CANARD AIRCRAFT down AOA
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System Size Resonance Associated with Canard Phenomenon in a Biological Cell System
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作者 Juan Ma Hong-ying Li +1 位作者 Zhong-huai Hou Hou-wen Xin 《Chinese Journal of Chemical Physics》 SCIE CAS CSCD 北大核心 2008年第6期521-525,共5页
The influence of internal noise on the calcium oscillations is studied. It is found that stochastic calcium oscillations occur when the internal noise is considered, while the corresponding deterministic dynamics only... The influence of internal noise on the calcium oscillations is studied. It is found that stochastic calcium oscillations occur when the internal noise is considered, while the corresponding deterministic dynamics only yields a steady state. Also,. the performance of such oscillations shows two maxima with the variation of the system size, indicating the occurrence of system size resonance. This behavior is found to be intimately connected with the canard phenomenon. Interestingly, it is also found that one of the optimal system sizes matches well with the real cell size, and such a match is robust to the variation of the control parameters. 展开更多
关键词 Internal noise Calcium oscillations System size resonance Canard phenomenon
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Canard Solutions in a Predator-Prey Model
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作者 Guojian Lin 《Journal of Applied Mathematics and Physics》 2022年第5期1678-1693,共16页
The canard explosion phenomenon in a predator-prey model with Michaelis-Menten functional response is analyzed in this paper by employing the geometric singular perturbation theory. First, some turning points, such as... The canard explosion phenomenon in a predator-prey model with Michaelis-Menten functional response is analyzed in this paper by employing the geometric singular perturbation theory. First, some turning points, such as, fold point, transcritical point, pitchfork point, canard point, are identified;then Hopf bifurcation, relaxation oscillation, together with the canard transition from Hopf bifurcation to relaxation oscillation are discussed. 展开更多
关键词 Canard Explosion Relaxation Oscillation Predator-Prey Model Geometric Singular Perturbation Theory
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Canard轨迹原理 被引量:8
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作者 徐云 张建峡 +1 位作者 徐霞 周红 《物理学报》 SCIE EI CAS CSCD 北大核心 2008年第7期4029-4033,共5页
为了精确的求出Canard轨迹的描述方程,提出了一个分段表达的非线性模型,能直接求出一个非线性二阶自治方程的相轨迹方程的解析解,能定量求出Canard轨迹的描述方程和参数条件,可以用两类方程简单描述所有的Canard轨迹.
关键词 非线性系统 Canard轨迹 弛张振荡
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Investigation of Vortex Interaction in Canard-FSW Configurations Based on the Numerical Wind Tunnel Method 被引量:1
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作者 张国庆 杨树兴 徐勇 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2010年第3期312-319,共8页
The vortex interference mechanism on low Reynolds number between the canard and main wing of the canard-forward sweep wing (Canard-FSW) configurations is simulated numerically by employing the numerical wind tunnel ... The vortex interference mechanism on low Reynolds number between the canard and main wing of the canard-forward sweep wing (Canard-FSW) configurations is simulated numerically by employing the numerical wind tunnel method. The variations of aerodynamic characteristics of Canard-FSW configurations with different positions of the canard are investigated,finding that the aerodynamic interference and mutual coupling effect between the canard and main wing have made great contributions to the lift and stability characteristics of the whole aircraft. Canard can radically improve the surface flow pattern of the main wing. And its own vortex can have a favorable interference on the main wing and can effectively control the airflow boundary layer separation. At small angles of attack,the aerodynamic characteristics are sensitive to the positions of the canard and the main wing,but at high angles of attack,the aerodynamic performances of the configuration are not only related to the shape of the canard (forward or backward),but also with the size of control force as well as the features of the vortices generated above the main wing and the canard. The different configurations and vortices are illustrated using the velocity vector,streamlines and pressure contours. 展开更多
关键词 cluster system Canard-FSW backward sweep canard forward sweep canard VORTEX interaction mesh
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单结管二阶自治电路中的Canard现象 被引量:3
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作者 徐云 《科学通报》 EI CAS CSCD 北大核心 1996年第16期1517-1519,共3页
在非线性动力学系统中,三阶以上的自治系统才能产生混沌运动,这使得有关非线性方面的研究集于三阶以上的自治系统(二阶以上的非自治系统)。然而,二阶自治系统内也会出现很复杂的动力学现象;文献[1]首先在数学研究中报道了Canard现象,而B... 在非线性动力学系统中,三阶以上的自治系统才能产生混沌运动,这使得有关非线性方面的研究集于三阶以上的自治系统(二阶以上的非自治系统)。然而,二阶自治系统内也会出现很复杂的动力学现象;文献[1]首先在数学研究中报道了Canard现象,而Braaksma等对细胞膜方程中的Canard现象进行了研究和报道。Canard现象的名称来源于相轨迹,形状像1只鸭子,它的产生过程简述如下:在含有非线性函数f(x)的二阶自治系统中,在控制参数的分岔点附近的一个邻域内,该系统的相图会出现象鸭子形状的极限环,随控制参数的变化,会出现无头鸭极限环(图1:acbda闭合路径);有头鸭极限环(图1:acbdea闭合路径);驰张振荡器极限环(图1:acba闭合路径)。我们用单结管作非线性元件构成一个二阶自治电路,发现了许多与文献[1]和文献[2]相同和不同的特点。 展开更多
关键词 非线性电路 晶体管 单结晶体管 Canard现象
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一氧化碳表面催化氧化反应中canard突变与内信号随机双共振
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作者 赵刚 侯中怀 辛厚文 《中国科学(B辑)》 CSCD 北大核心 2005年第4期268-274,共7页
Canard突变是普遍存在于可激发体系内的一种复杂时间行为,其特征表现为极限环振幅与周期在极小的参数范围内急剧变化.分析了在超临界霍普夫分叉附近canard突变的动力学行为及其对噪声的响应特性,发现并说明了Pt(110)/CO+O2表面催化氧化... Canard突变是普遍存在于可激发体系内的一种复杂时间行为,其特征表现为极限环振幅与周期在极小的参数范围内急剧变化.分析了在超临界霍普夫分叉附近canard突变的动力学行为及其对噪声的响应特性,发现并说明了Pt(110)/CO+O2表面催化氧化反应体系中的内信号随机双共振,这是一种噪声对不同频率信号的选择性放大作用. 展开更多
关键词 内信号随机双共振 canard突变 Pt(1lO)/CO+02表面催化氧化反应 可激发体系 零线 催化氧化反应 频率信号 双共振 突变 一氧化碳
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