By Luigi Fortuna, Mattia Frasca, Maria Gabriella Xibilia
Because the beginning of the Chua circuit in 1983, quite a few fruitful, interesting and appropriate examine issues have arisen. In honor of the twenty fifth anniversary of the discovery of Chua's circuit, this ebook provides the 25 years of analysis at the implementation of Chua's circuit, and in addition discusses destiny instructions and rising functions of modern effects. the aim of the ebook is to supply researchers, PhD scholars, and undergraduate scholars a examine monograph containing either basics at the subject matters and complicated effects which have been lately acquired. With approximately 60 illustrations incorporated within the e-book, it additionally indicates the specific schematics of numerous various implementations that may be simply reproduced with a reasonably cheap experimental setup and PC-based size instrumentation. Contents: The beginning of Chua's Circuit Implementations of Chua's Diode mobile Nonlinear Networks and Chua's Circuit Frequency Switched Chua's Circuit: Experimental Dynamics Characterization Programmable Chua's Circuit Switched Capacitor-based Chua's Circuit The Four-Element Chua's Circuit The natural Chua's Circuit functions of Chua's Circuit
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Additional info for Chua's circuit implementations: yesterday, today, and tomorrow
Hyperchaos is a chaotic behavior in which two or more Lyapunov exponents are positive. As such to be observed in an autonomous circuit it needs at least a fourth-order system. In [Cannas and Cincotti (2002); Cincotti and Stefano (2004)] it is shown that two bidirectionally coupled Chua’s circuits can generate hyperchaos. A nonlinear resistor is used to couple the two circuits. circuit February 10, 2009 17:2 World Scientific Book - 9in x 6in The birth of the Chua’s circuit circuit 41 The experimental observation of hyperchaos in coupled Chua’s circuits is reported in [Kapitaniak et al.
4 The n-scroll chaotic attractor In [Suykens and Vandewalle (1993)] it is shown how, by modifying the characteristic of the nonlinear resistor, the Chua’s circuit can be generalized to a circuit exhibiting more complex attractors. The nonlinearity is modiﬁed by introducing additional breakpoints. The attractor generated in this way is a generalization of the double scroll strange attractor called n-scroll chaotic attractor or a multiscroll chaotic attractor with n = 1, 2, 3, . .. In this context the double scroll strange attractor corresponds to the 1- double scroll.
22 35 Another canonical member of the Chua’s circuit family. Given the set of eigenvalues µ1 , µ2 , µ3 , ν1 , ν2 and ν3 of the member of the Chua’s circuit family to be synthesized, the parameters of the canonical circuit of Fig. 41) −1 G = KC2 a (p3 −q3 ) with K = −L p3 + G C1 (p1 −q1 ) . In this case the constraint p1 = q1 should be satisﬁed, which again deﬁnes a set of zero measure. We notice that for some values of the eigenvalues set to be implemented, the parameters of the Chua’s oscillator may assume negative values.