Safety margin criterion of nonlinear unbalance elastic axle system

IntroductionAtpresentanewanddevelopingsubject—chaoticdynamicsstartsabroadprospectforanalysisofnonlinearsystem[1～ 5 ].Largerotatingmachineryisatypicalnonlinearnon_autonomoussystem .Thesaferunofrotorsystemisofgreatsignificancetosociallifeandeconomicdevelopment.Thestabilityisthekeytosafeoperation .Thesafestabilityanalysisandcontrolforlargesystemisnotonlyamajorbasicresearchbutalsoisveryimportanttosolvethesafeproblemsinlifeandproduction[6 ,7].Soar,althoughmanymathematicians,mechanistsandengineer…     

非线性碰摩力对碰摩转子分叉与混沌行为的影响

研究了具有非线性碰摩力的转子局部碰摩的分叉与混沌运动,利用计算机仿真对某发动机转子的碰摩故障进行了数值模拟,讨论了转子系统参数的变化对转子混池运动状态的影响,并与碰摩实验结果进行了比较,发现了具有非线性碰摩力的转子局部碰摩转子系统的各种多周期运动和混沌运动及其演变过程。     

混沌系统延迟反馈控制的理论与实验研究

综述了近年来控制混沌的延迟反馈控制技术------DFC控制的相关进展,总结了延迟反馈控制在不动点和不稳定周期轨道镇定方面的局限性和可控性研究的理论成果,介绍了延迟反馈控制在电子线路和磁弹性梁混沌控制方面的实验,并对延迟反馈控制技术未来的研究方向和发展前景进行了预测和展望。      

一种超混沌映射的单双参量自适应同步

利用参量自适应法实现了超混沌系统Kawakami映射的同步.通过严密的数学推导,给出了Kawakami映射在单参量自适应下实现同步的充分条件,并在双参量自适应控制下系统同样实现了同步.数值模拟结果显示,该映射输出具有类似于白噪声的宽谱特性,因此比较适合用于保密通信.     

受迫振动非线性特性的教学拓展

受迫振动在大学物理和大学物理实验中均是重点教学内容,为了使学生更加深入理解受迫振动的非线性特性,本文基于波耳共振仪所涉及的非线性因素和实验数据,对受迫振动方程进行非线性修正,利用数值分析探讨其非线性特性.通过引入硬弹簧型杜芬方程,探讨系统由周期性运动进入混沌状态的演化,将受迫振动中相对稳定的平衡点与奇异吸引子进行类比,...     

Diffusion in fluids with large mean free paths: Non-classical behavior between Knudsen and Fickian limits

Diffusion in fluids is analyzed at non-classical conditions, intermediate between the Knudsen and Fickian limits. The fluid is considered in the framework of the Einstein’s diffusion evolution equation involving expansions of the density distribution in powers of displacement and time. The standard truncation of these expansions results in the classical model of diffusion; however, higher-order terms lead to a departure from classical behavior. This has not been studied or discussed adequately in the literature previously.Here, we present an exact solution of the Einstein’s diffusion evolution equation without truncation of the density expansions. This solution illustrates limitations in the classical truncations and demonstrates non-classical effects due to large mean free paths, λ. In particular, this new solution shows that, at large λ, there are significant quantitative deviations from classical diffusion profiles. In addition, this solution demonstrates a dramatic change in the diffusion mechanism from the state where the molecular motions are predominantly ballistic to one of molecular chaos. This has implications for fundamentals of fluids between the Knudsen and Fickian limits, and for a variety of fields where evolution of a system includes random, multi-scale displacement of particles, such as nanotechnology, vacuum techniques, turbulence, and astrophysics.     

Adaptive synchronization of weighted complex dynamical networks through pinning

This paper considers the problem of controlling weighted complex dynamical networks by applying adaptive control to a fraction of network nodes. We investigate the local and global synchronization of the controlled dynamical network through the construction of a master stability function and a Lyapunov function. Analytical results show that a certain number of nodes can be controlled by using adaptive pinning to ensure the synchronization of the entire network. We present numerical simulations to verify the effectiveness of the proposed scheme. In comparison with feedback pinning, the proposed pinning control scheme is robust when tested by noise, different weighting and coupling structures, and time delays.     

Synchronization of different chaotic systems via active radial basis functions sliding mode controller

This paper presents a new method to synchronize different chaotic systems with disturbances via an active radial basis function （RBF） sliding controller. This method incorporates the advantages of active control, neural network and sliding mode control. The main part of the controller is given based on the output of the RBF neural networks and the weights of these single layer networks are tuned on-line based on the sliding mode reaching law. Only several radial basis functions are required for this controller which takes the sliding mode variable as the only input. The proposed controller can make the synchronization error converge to zero quickly and can overcome external disturbances. Analysis of the stability for the controller is carried out based on the Lyapunov stability theorem. Finally, five examples are given to illustrate the robustness and effectiveness of the proposed synchronization control strategy.     

Hash function based on the generalized Henon map

A new Hash function based on the generalized Henon map is proposed. We have obtained a binary sequence with excellent pseudo-random characteristics through improving the sequence generated by the generalized Henon map, and use it to construct Hash function. First we divide the message into groups, and then carry out the Xor operation between the ASCII value of each group and the binary sequence, the result can be used as the initial values of the next loop. Repeat the procedure until all the groups have been processed, and the final binary sequence is the Hash value. In the scheme, the initial values of the generalized Henon map are used as the secret key and the messages are mapped to Hash values with a designated length. Simulation results show that the proposed scheme has strong diffusion and confusion capability, good collision resistance, large key space, extreme sensitivity to message and secret key, and it is easy to be realized and extended.     

Controlling bifurcations and chaos in discrete small-world networks

We propose an impulsive hybrid control method to control the period-doubling bifurcations and stabilize unstable periodic orbits embedded in a chaotic attractor of a small-world network. Simulation results show that the bifurcations can be delayed or completely eliminated. A periodic orbit of the system can be controlled to any desired periodic orbit by using this method.