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1.
Theoretical and experimental study of Chen chaotic system with notch filter feedback control
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Since the past two decades, the time delay feedback control method has attracted more and more attention in chaos control studies because of its simplicity and efficiency compared with other chaos control schemes. Recently, it has been proposed to suppress low-dimensional chaos with the notch filter feedback control method, which can be implemented in a laser system. In this work, we have analytically determined the controllable conditions for notch filter feedback controlling of Chen chaotic system in terms of the Hopf bifurcation theory. The conditions for notch filter feedback controlled Chen chaoitc system having a stable limit cycle solution are given. Meanwhile, we also analysed the Hopf bifurcation direction, which is very important for parameter settings in notch filter feedback control applications. Finally, we apply the notch filter feedback control methods to the electronic circuit experiments and numerical simulations based on the theoretical analysis. The controlling results of notch filter feedback control method well prove the feasibility and reliability of the theoretical analysis. 相似文献
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Stability and Hopf bifurcation of a nonlinear electromechanical coupling system with time delay feedback
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The stability and the Hopf bifurcation of a nonlinear electromechanical coupling system with time delay feedback are studied.By considering the energy in the air-gap field of the AC motor,the dynamical equation of the electromechanical coupling transmission system is deduced and a time delay feedback is introduced to control the dynamic behaviors of the system.The characteristic roots and the stable regions of time delay are determined by the direct method,and the relationship between the feedback gain and the length summation of stable regions is analyzed.Choosing the time delay as a bifurcation parameter,we find that the Hopf bifurcation occurs when the time delay passes through a critical value.A formula for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is given by using the normal form method and the center manifold theorem.Numerical simulations are also performed,which confirm the analytical results. 相似文献
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分析一个简单二阶延迟系统的Hopf分支和混沌特性, 包括分支点、分支方向和分支周期解的稳定性, 解析求出退延迟情况下, 这个系统的相轨线方程; 通过数值计算并绘制分岔图, 揭示系统存在由倍周期通向混沌的道路; 利用单路线性组合信号, 反馈控制实现系统的部分完全同步; 利用主动-被动与线性反馈的联合, 实现系统的完全同步; 设计和搭建系统的电子实验线路, 并从实验中观测到与理论分析或数值计算相一致的结果.
关键词:
延迟非线性系统
电路实验
Hopf分支
混沌 相似文献
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By introducing an additional state feedback into a
three-dimensional autonomous chaotic attractor Lü system, this
paper presents a novel four-dimensional continuous autonomous
hyper-chaotic system which has only one equilibrium. There are only
8 terms in all four equations of the new hyper-chaotic system, which
may be less than any other four-dimensional continuous autonomous
hyper-chaotic systems generated by three-dimensional (3D) continuous
autonomous chaotic systems. The hyper-chaotic system undergoes Hopf
bifurcation when parameter c varies, and becomes the 3D modified
Lü system when parameter k varies. Although the hyper-chaotic
system does not undergo Hopf bifurcation when parameter k varies,
many dynamic behaviours such as periodic attractor, quasi periodic
attractor, chaotic attractor and hyper-chaotic attractor can be
observed. A circuit is also designed when parameter k varies and
the results of the circuit experiment are in good agreement with those
of simulation. 相似文献
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This letter puts forward an ingenious feedback control method with parametric delay to manipulate bifurcation control for a delayed fractional dual congestion model. By employing time delay as a bifurcation parameter, the local dynamics involving stability and Hopf bifurcation is examined. The control efforts can be realized with or without time delay in the strength of feedback control. It suggests that the stability performance is consumedly elevated by exploiting the parametric delay feedback controller, yet Hopf bifurcation engenders ahead of time in the event of the absence of the controller. Moreover, the impact of the order or linear feedback gain on the bifurcation point is numerically discussed via aborative calculation. Numerical simulations are eventually actualized to corroborate the proposed scheme. 相似文献
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We perform bifurcation analysis in a complex Ginzburg–Landau system with delayed feedback under the homogeneous Neumann boundary condition. We calculate the amplitude death region, and it turns out that the boundary of the amplitude death region consists of two Hopf bifurcation curves with wave number zero. The existence conditions for double Hopf bifurcations are established. Taking the feedback strength and time delay as bifurcation parameters, normal forms truncated to the third order at double Hopf singularity are derived, and the unfolding near the critical points is given. The bifurcation diagram near the double Hopf bifurcation is drawn in the two-parameter plane. The phenomena of amplitude death, the existence of stable bifurcating periodic solutions, and the coexistence of two stable periodic solutions with fast oscillation and slow oscillation respectively are simulated. 相似文献
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A novel four-wing chaotic attractor generated from a three-dimensional quadratic autonomous
system 总被引:2,自引:0,他引:2
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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. 相似文献
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基于数学上延迟(时滞)系统Hopf分支理论及分析方法,解析地确定出 用延迟反馈法可控制三阶自治混沌系统的一般条件.利用这种分析方法,着重从理论上 讨论了在控制意义下系统出现稳定周期解及由Hopf分支产生周期解的分支方向的判据.将这 些理论应用到三阶自治混沌系统的控制实例中,解析地得到使系统可控的参量区域.在该区 域内选择控制参量,通过数值模拟也得到控制系统从混沌到周期态的结果.
关键词:
延迟反馈
Hopf分支
控制混沌 相似文献
14.
对应于混沌振子的各个Lyapunov指数,在切空间中定义了广义相位和广义旋转数.广义旋转数和Lyapunov指数相结合,可以更完整地描述混沌吸引子的各个运动模式的运动特征,包括伸缩与旋转.用耦合Duffing振子研究了时空混沌系统在同步混沌失稳时发生的分岔行为.结果表明,耦合振子的同步混沌态可以发生一种Hopf分岔,在Hopf分岔后,系统的功率谱中出现了一个特征频率,其值恰好等于分岔前临界横模的广义旋转数.
关键词: 相似文献
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In this paper, we investigate the problem of Hopf bifurcation and chaos control in a new chaotic system. A hybrid control strategy using both state feedback and parameter control is proposed. Theoretical analysis shows that the Hopf bifurcation critical value can be changed via hybrid control. Meanwhile, this control strategy can also control the chaos state. The direction and stability of bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem. Finally, numerical simulations are carried out to illustrate the effectiveness of the main theoretical results. 相似文献
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利用荷控忆阻器和一个电感串联设计一种新型浮地忆阻混沌电路.用常规动力学分析方法研究该系统的基本动力学特性,发现系统可以产生一对关于原点对称的"心"型吸引子.将观察混沌吸引子时关注的电压、电流推广到功率和能量信号,观察到蝴蝶结型奇怪吸引子的产生.理论分析Hopf分岔行为并通过数值仿真进行验证,结果表明系统随电路参数变化能产生Hopf分岔、反倍周期分岔两种分岔行为.相对于其它忆阻混沌电路该电路采用的是一个浮地型忆阻器,并且在初始状态改变时,能产生共存吸引子和混沌吸引子与周期极限环共存现象. 相似文献
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This paper is concerned with the Hopf bifurcation control of a newhyperchaotic circuit system. The stability of the hyperchaotic circuit system depends on a selected control parameter is studied, and the critical value of the system parameter at which Hopf bifurcation occurs is investigated. Theoretical analysis give the stability of the Hopf bifurcation. In particular, washout filter aided feedback controllers are designed for delaying the bifurcation point and ensuring the stability of the bifurcated limit cycles. Animportant feature of the control laws is that they do not result in any change in the set of equilibria. Computer simulation results are presented to confirm the analytical predictions. 相似文献