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Fractional dynamic system research in China

Fractional dynamic system research in China. --- Symposium of fractional dynamic system and its applications in China Mechanic conference. Reporter: Hongguang Sun. Center for Self-Organizing and Intelligent Systems (CSOIS), Utah State University

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Fractional dynamic system research in China

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  1. Fractional dynamic system research in China ---Symposium of fractional dynamic system and its applications in China Mechanic conference Reporter: Hongguang Sun Center for Self-Organizing and Intelligent Systems (CSOIS), Utah State University Institute of Soft Matter Mechanics, Hohai University, China

  2. Information about conference • Name: Academic Conference of China Society of Mechanics • Time: Aug.22—Aug.26, 2009 • Location: ZhengZhou, China • Papers: more than 1500 • It is the highest-level conference of China Society of Mechanics

  3. Here

  4. Fractional dynamics and its applications • Organizers: Keqin Zhu, Wen Chen, Changpin Li • Number of submitted articles: 28; • Full-length paper: 21;

  5. Paper classification • Theoretical research: 8 • Numerical methods: 6 • Modeling approaches: 5 • Application research:8 • Others: 1 English articles: 2 Chinese articles: 26

  6. Some new and interesting results

  7. Yang, Pan, Zhu, Keqin (Tsinhua University) Constitutive equation for the generalized upper convected Maxwell model Fractional UCM model Where is inverse factor of stress; Is inverse factor of strain; l is relaxation time; E is displacement gradient; a, b are fractional differential orders.

  8. The integral expression of UCM constitutive model The expression of the G has the following form

  9. Research on dynamical analysis of fractional nonlinear systems and typical complex behaviors induced by numerical algorithm Liu, Jie, Dong, Pengzhen and Shang Gang (Wuhan University) • The widely used Charefand, Oustloup methods may cause fake chaotic or fake periodic phenomena under some wrong conditions • The modified Oustloup method can prove the ability of traditional frequency method They first considered Liu system (q=0.8)

  10. Fake Simulation result of fractional Liu system, q=0.8. Left: Charefand method, Right: improved Oustaloup Moreover, they investigated the Lü system (q=0.86)

  11. The ADM predictor-corrector scheme may cause fake complex behaviors while using unsuitable length of iteration step. Fake Simulation result of fractional Lü system with q=0.86, Left: △t=0.01; Right: △t=0.001

  12. Stability analysis of fractional differential equation and its application in HIV-1 infection modeling Kou, Chunhai, Yan, Ye and Liu, Jian (Donghua University) They make an investigation of fractional model of HIV-1 infection. Finally they get some valuable results. (Full length paper is unavailable) Main contributions:

  13. Fractional Order Robust Control of Four Wheel Steering Vehicle Based on Yaw Rate Tracking Chen, Ning, Chen, Ye, Chen, Nan (Nanjing Forestry University) The fractional order PIλDμ robust control is applied in the yaw rate tracking control of four-wheel-steering vehicle in this paper to improve the robustness of yaw rate response for vehicle with uncertain parameters Control map

  14. The function of fractional PID control The response curves of step inputs of three types of vehicle angular

  15. Time-dependent Fractional Schrödinger Equation with Moving Boundary Jiang, Xiaoyun, Xu, Mingyu (Jiang Xiaoyun) The considered time-dependent fractional spatial Schrödinger equation The moving-boundary problem is transformed into a fixed-boundary problem and a new Hamiltonian is obtained by means of Generalized Canonical Transformations The time evolution behaviors of quantum states are described by means of time-dependent perturbation theory

  16. Bound estimation of Lyapunov parameter in fractional system Li, Changpin, Gong, Ziqing, Qian Deliang (Shanghai University) • Bound estimation of Lyapunov parameter in Riemann and Caputo types of fractional system • The upper bound of fractional system is achieved, the existence of the lower bound of fractional system is illustrated by an example Main contributions:

  17. Stationary response of Duffing oscillator with fractional derivative damping under combined harmonic and wide band noise excitations • The averaged Itô stochastic differential equations for duffing oscillator with fractional derivative damping under combined harmonic and wide band noise excitations are obtained by using the generalized harmonic functions • The stationary response is obtained by solving the reduced PFK equation Chen, Lincong, Zhu, Weiqiu (Tsinhua University) Main contributions:

  18. Generations and mechanisms of multi-stripes fractional order chaotic attractors Yang, Shuiping, Wu, Jianxin, Li, Min, Xiao, Aiguo, Fu, Jingli (Xiangtan university) • The original fractional order chaotic attractors was turned into a pattern with multiple “parallel” or “ rectangular” stripes by employing simple periodic nonlinear functions • Theoretic analysis about the underlying mechanism of generating the parallel stripes in the fractional order attractors is given • Period doubling routes to chaos in the fractional order Rossler equation are also found Main contributions

  19. Identification of constitutive parameters of a visco-elastic rod with generalized Voigt fractional derivatives constitutive relations • The ant colony algorithm is proposed to solve constitutive parameters inverse problems of a visco-elastic rod with generalized Voigt fractional derivatives constitutive relations Yang, Haitian and Zhao, Xiao (Dalian University of Technology) Main contributions:

  20. The anomalous diffusion of calcium sparks in cardiac cell Tan, Wenchang (Peking University) • Cytoplasm belongs to visco-elastic fluid • Propose the spatial fractional diffusion equation model for diffusion process of calcium sparks in cardiac cell Main contributions:

  21. IFAC Workshop on Fractional Differentiation and its Application • First: France, 2004; • Second: Portugal, 2006; • Third: Turkey, 2008; • Fourth: Spain, Lisbon, 2010; • Fifth: China, Nanjing, 2012. Welcome to China in 2012

  22. Paper list • Shen Shujun, Liu Fawang, Solution techniques for the riesz space-time fractional advection dispersion equation. • Zhang Xiaodi, Wen Chen, A comparison of relaxation-oscillation models involving fractal, fractional and positive fractional derivatives. • Liu QingXia, Finite element approximation for the anomalous sub-diffusion process • Yang Pan, Zhu Ke Qin, Investigation on the constitutive relationship for the generalized UCM model • Chen Wen, Introduction of FDA 2008 • Liu Jie, Dong Pengzhen and Shang Gang, Research on dynamical analysis of fractional nonlinear Systems and typical complex behaviours induced by numerical algorithm • Hu Kaixin, Zhu Keqin, A Study of Mechanical Analogues of Fractional Elements • Sun Hongguang and Chen Wen, Fractional differential equation models of complex anomalous diffusion

  23. Wang Zaihua, General solution of a linear vibration system with fractional-order derivative • Chen Ning, Chen Ye, Chen Nan, Fractional order robust control of four wheel steering vehicle based on yaw rate tracking • Li Xicheng, A fractional mathematical model of pharmacokinetics for percutaneous absorption • Wei Hui, Chen Wen, Sun Hongguang, The inverse source problem of space fractional abnormal diffusion equations • Liang, Yongshun and Zhang, Qi, Definition of fractal functions and their fractional integral • Jiang Xiaoyun and Xu Mingyu, Time-dependent fractional schrödinger equation with moving boundary • Su Li-juan, A finite difference method for the two-sided space-fractional advection-diffusion equation • Chen Lin-cong and Zhu Wei-qiu, Stationary response of Duffing oscillator with fractional derivative damping under combined harmonic and wide band noise excitations

  24. Yang Shuiping, Wu Jianxin, Li Min, Xiao Aiguo and Fu Jingli, Generations and mechanisms of multi-stripes fractional order chaotic attractors • Hao Wuling, Zhang Wei and Hao Junjun, The analytic expressions of one class of fractalcurve • Zhao Xiao, Yang Haitian, Identification of constitutive parameters of a visco-elastic rod with generalized Voigt fractional derivatives constitutive relations • Liu Yaqing, Zheng Liancun and Zhang Xinxin, Exact Solution for MHD flow of a generalized unsteady couette fluid • Tan, Wenchang, The anomalous diffusion of calcium sparks in cardiac cell • Li Changpin, Gong Ziqing and Qian Deliang, Bound estimation of Lyapunov parameter in fractional system • Kou, Chunhai, Yan, Ye and Liu, Jian, Stability analysis of fractional differential equation and its application in HIV-1 infection modeling • Zhu Keqin, Hu Kaixin and Yang Fan, Viscous and elastic effects in the fractional elemental model

  25. Yin Deshen and Chen Wen, The volumetric strain research of soil in the conventional three-axis experiment based on fractional calculous • Chen Ning and Tai Yongpeng, fractional semi-active suspension control of vehicles based on sliding mode observer • Pan Xinyuan and Xiao Aiguo, Asymptotic stability of numerical methods of two types of fractional order functional differential equations • Chen Ming and Yin Xiezhen, Finite element model of relaxation properties of fin material

  26. Thank you HongGuang Sun:sunhongguang08@gmail.com Website of fractional dynamics: http://www.ismm.ac.cn/ismmlink/PLFD/index.html

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