Chua's circuit implementations: yesterday, today, and by Luigi Fortuna, Mattia Frasca, Maria Gabriella Xibilia

By Luigi Fortuna, Mattia Frasca, Maria Gabriella Xibilia

Because the delivery of the Chua circuit in 1983, a variety of fruitful, attention-grabbing and proper examine issues have arisen. In honor of the twenty fifth anniversary of the discovery of Chua's circuit, this booklet provides the 25 years of analysis at the implementation of Chua's circuit, and likewise discusses destiny instructions and rising purposes of contemporary effects. the aim of the booklet is to supply researchers, PhD scholars, and undergraduate scholars a study monograph containing either basics at the themes and complicated effects which were lately acquired. With approximately 60 illustrations integrated within the booklet, it additionally exhibits the distinctive schematics of numerous various implementations that may be simply reproduced with a inexpensive experimental setup and PC-based dimension 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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Example text

5, it is enough to take into account the three segment nonlinearity. This is no more true when the behavior of the Chua’s circuit at different initial conditions is investigated or a bifurcation analysis is carried on. In fact, when the three segment nonlinearity is considered, for large initial conditions the behavior of the system may be unstable, which is clearly not the case of the real circuit. When the five segment nonlinearity is taken into account, it can be demonstrated that the double scroll attractor coexists with a stable external limit cycle and that an unstable saddle-type periodic orbit separates the basins of attraction of the two attractors.

Circuit 29 Bifurcation diagram with respect to β. The other parameters are as in Eq. 23)    a11 a12 a13 b1 with A =  a21 a22 a23  and b =  b2  in regions D1 and D−1 and a31 a32 a33 b3   α11 α12 α13 A0 =  α21 α22 α23  in region D0 . α31 α32 α33 Although 21 parameters appear in Eqs. 23), taking into account the constraint that the vector field is continuous, only 12 parameters can be arbitrarily fixed. For this reason the Chua’s circuit family is a 12-parameter family. , able to qualitatively reproduce the dynamics of any member of the family.

E. when two or more chaotic circuits follow the same chaotic trajectory. Since chaotic systems exhibit high sensitivity to initial conditions and thus, even if identical and, possibly, starting from almost the same initial points, follow trajectories which rapidly become uncorrelated, appropriate techniques should be set up to obtain complete synchronization. Such techniques to couple two or more chaotic circuits can be mainly divided into two classes: drive-response (or unidirectional) coupling and bidirectional coupling.

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