Fritz Colonius's Dynamics, Bifurcations and Control PDF

By Fritz Colonius

This e-book includes a number of the papers awarded on the third NCN Workshop which used to be involved in "Dynamics, Bifurcations and Control". The peer-reviewed papers describe a few methods how dynamical structures innovations may be utilized for research and layout difficulties up to speed with themes starting from bifurcation keep an eye on through balance and stabilizaton to the worldwide dynamical behaviour of keep an eye on structures. The booklet supplies an summary of the present prestige of the sector.

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Extra resources for Dynamics, Bifurcations and Control

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Alamo. Global stability analysis of second-order fuzzy control systems. In R. Palm, D. Driankov, and H. Hellendorn, editors, Advances in Fuzzy Control, pages 11{31. Physica-Verlag, 1997. 2. J. Aracil, E. Ponce, and T. Alamo. A frequency-domain approach to bifurcations in control systems with saturation. International Journal of Systems Science, 31(10):1261{1271, 2000. 3. P. Atherton. Nonlinear Control Engineering. Describing Function Analysis and Design. Van Nostrand Reinhold, 1975. 4. F. Bonani and M.

In the present work the averaged model of Gross 4] for near-resonant perturbation of a general low order F. Colonius, L. ): Dynamics, Bifurcations, and Control, LNCIS 273, pp. 51−65, 2002. A. Hassouneh, H. H. Abed system undergoing Hopf bifurcation is used to derive a formula for the parameter shift at the bifurcation. It is shown that this quantity is proportional to the stability coe cient of the bifurcation when resonant forcing is applied to the system. The proportionality factor is a function of the amplitude of the forcing signal and characteristic system parameters, and is always negative.

The use of an approximate method, the describing function, greatly simpli es the analysis. It should be emphasized the huge amount of information about the system behaviour summarized in Fig. 8 and that is inherent in Fig. 6. In this way it supplies a global perspective on the behaviour of the system. 46 F. Gordillo, I. Alcalá, and J. Aracil 01 11 00 10 01 a) Fig. 8. b) 11 00 11 00 c) d) Schematic representation of a saddle-node bifurcation of periodic orbits. 2 Subcritical Hopf bifurcation at in nity Consider the same structure than in Fig.

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