Nonlinear Dynamics Part 7

Tham khảo tài liệu 'nonlinear dynamics part 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Dynamics and Control of Nonlinear Variable Order Oscillators 143 and illustrate its behavior as compared to the classical Duffing equation. Exact feedback linearization is used to derive a linear controller of the Duffing equation with variable order damping. Finally a variable order controller is used to suppress chaos on the Lorenz system of equations. To the best knowledge of the authors this is the first time a variable order controller is described. 6. References Charef A. Sun . Tsao . Onaral B. 1992 Fractal system as represented by singularity function IEEE Transactions on Automatic Control 37 9 1465-1470. Coimbra Kobayashi . 2002 . On the Viscous Motion of a Small Particle in a Rotating Cylinder. Journal of Fluid Mechanics 469 pp. 257-286. Coimbra . 2003 Mechanics with variable-order differential operators Annalen der Physik 12 11-12 692-703. Coimbra . L Esperance D. Lambert A. Trolinger . Rangel . 2004 An experimental study on the history effects in high-frequency Stokes flows Journal of Fluid Mechanics 504 353-363. Diaz G. Coimbra . 2009 Nonlinear dynamics and control of a variable order oscillator with application to the van der Pol equation Nonlinear Dynamics 56 145-157. Diethelm K. N. J. Ford . Freed . 2002 A predictor-corrector approach for the numerical solution of fractional differential equations Nonlinear Dynamics 29 2002 3-22. Diethelm K. Ford . Freed . Luchko Y. 2005 Algorithms for the fractional calculus A selection of numerical methods Computational Methods in Applied Mechanics and Engineering 194 6-8 743-773. Drazin . 1994 Nonlinear Systems Cambridge Texts in Applied Mathematics Cambridge University Press UK. Grigorenko I Grigorenko E. 2003 Chaotic dynamics of the fractional Lorenz system. Physical Review Letters 91 3 . Guckenheimer J. Holmes P. 1983 Nonlinear Oscillators Dynamical Systems and Bifurcations of Vector Fields Applied Mathematical Sciences 42 Spriner-Verlag New .