Download Dynamics, Bifurcations and Control by Fritz Colonius PDF

By Fritz Colonius

ISBN-10: 3540428909

ISBN-13: 9783540428909

This booklet incorporates a number of the papers provided on the third NCN Workshop which was once desirous about "Dynamics, Bifurcations and Control". The peer-reviewed papers describe a couple of methods how dynamical platforms suggestions may be utilized for research and layout difficulties on top of things with issues starting from bifurcation regulate through balance and stabilizaton to the worldwide dynamical behaviour of keep watch over platforms. The ebook supplies an outline of the present prestige of the sphere.

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Example text

7) in polar coordinates. 0 + = 1 + . Gross used the following variable and parameter scalings r = "r, = "2 , k = "3 k, = "2 , = + cos 1 ( (A22VB1 ) ) along with the time scaling t = "2 t. Here V = 12 (A1 + B2 )2 + (A2 B1 )2 ]1=2 . 0 = 1. The latter assumption implies that the small parameter can be viewed as a detuning factor. Eq. (8) can be considered as a perturbation of the system of the form (3). For k = 0 the averaged model is exactly of the form (3) and the vector eld corresponding to the amplitude variable r is decoupled from the phase variable .

Depending on the initial condition the nonlinear system evolves towards the desired operating point (the origin) or towards the stable limit cycle. The reader may be surprised that the orbits intersect for a two dimensional G(s). The reason is that the dimension if the system is higher than 2 since the rate limiter is dynamical (remember remark 1). a)) the desired operating point is stable. The e ect of these intersections is that the stability is only local with a bounded attraction basin due to the existence Bifurcations in Systems with a Rate Limiter 45 8 30 25 6 20 4 15 2 x2 x2 10 5 0 0 −2 −5 −4 −10 −15 −15 −10 −5 0 x1 Kp = 7 Fig.

Describing Function Analysis and Design. Van Nostrand Reinhold, 1975. 4. F. Bonani and M. Gilli. Analysis of stability and bifurcations of limit cycles in chua's circuit through the harmonic-balance approach. IEEE Trans. on Circuits and Systems I- Fundamental Theory and Applications, 46(8):881{890, 1999. 5. A. Cook. Nonlinear Dynamical Systems. Prentice Hall, 1994. 6. A. E. Vander Velde. Multiple-input Describing Functions and Nonlinear Systems Design. Prentice-Hall, 1968. 7. K. Hale and H. Kocak.

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Dynamics, Bifurcations and Control by Fritz Colonius


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