By Schoell E., Schuster H.G. (eds.)
ISBN-10: 3527406050
ISBN-13: 9783527406050
This long-awaited revised moment version of the traditional reference at the topic has been significantly elevated to incorporate such contemporary advancements as novel regulate schemes, keep an eye on of chaotic space-time styles, keep watch over of noisy nonlinear platforms, and conversation with chaos, in addition to promising new instructions in study. The contributions from best overseas scientists lively within the box supply a accomplished evaluation of our present point of data on chaos keep watch over and its functions in physics, chemistry, biology, drugs, and engineering. moreover, they exhibit the overlap with the normal box of regulate thought within the engineering community.An interdisciplinary technique of curiosity to scientists and engineers operating in a couple of parts.
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Sample text
1 Diode circuit: the diode circuit is composed of an AC voltage source Vin , a resistor R, an inductor L, and a diode; Vd is the voltage across the diode. 1:14 13 14 1 Controlling Chaos where V0 is the voltage amplitude and f is the frequency. For the diode, we consider its high-frequency model for the voltage across it, which is given by [19, 40] Vd jqj Cj À Cd q Cj Cd E0 ; 2Cj Cd 2Cj Cd 1:15 where q is the diode accumulated charge, Cj is the junction capacitance, and Cd is the diffusion capacitance.
Our goal is to steer it to another periodic orbit Xb . The LQ controller drives the trajectory from Xa to a point Xnfa near Xfa. In Xnfa a small perturbation is applied, and the system moves to the state Xfa . Another perturbation is applied, and the system moves to the state Xfa . Our chaotic targeting procedure is then used to stir the system to Xtb . Another small perturbation drives the system to the point Xob , that belongs to the basin of attraction of Xb . From this point, the system’s natural dynamics drives the trajectory to the desired stable periodic orbit Xb .
Physica D, 81:280–294, 1995. E. M. Bollt and J. D. Meiss. Targeting chaotic orbits to the moon through recurrence. Phys. Rev. A, 204:373–378, 1995. B. V. Chirikov. A universal instability of many-dimensional oscillator systems. Phys. , 52:265–379, 1979. D. L. DeAngelis, W. M. Post, and C. C. Travis. Positive Feedback in Natural Systems. Springer, Berlin, 1986. R. Devaney. An Introduction to Chaotic Dynamical Systems. Persus Books, Cambridge, MA, 1989. W. L. Ditto, S. N. Tauseo, and M. L. Spano.
Handbook of Chaos Control by Schoell E., Schuster H.G. (eds.)
by Joseph
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