By Luigi Fortuna, Mattia Frasca, Maria Gabriella Xibilia

Because the beginning of the Chua circuit in 1983, a number of fruitful, interesting and proper learn themes have arisen. In honor of the twenty fifth anniversary of the discovery of Chua's circuit, this booklet offers 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 booklet is to supply researchers, PhD scholars, and undergraduate scholars a study monograph containing either basics at the themes and complicated effects which have been lately got. With approximately 60 illustrations incorporated within the publication, it additionally indicates the unique schematics of a number of various implementations that may be simply reproduced with a inexpensive 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 purposes of Chua's Circuit

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**Sample text**

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.

50) Feedback control of the Chua’s oscillator [Chen (1993)]. In the linear feedback technique the controller has a simple structure and does not need the access to the system parameters, but requires the access to many state variables. 48) with K11 = α(m0 − 1), K22 = 1 and K33 = 0 for t ≥ 50. Fig. 34 shows the trend of the x variable, showing how the equilibrium point P + is indeed stabilized. 3 2 x 1 0 −1 −2 −3 0 Fig. 34 50 100 t 150 200 Example of feedback control of the Chua’s oscillator: stabilization of P + .

Fm (u)) and H = (Fm+1 (u), . . , Fn (u)). , w(t) and w (t) asymptotically have the same evolution) if all the Lyapunov exponents of the subsystem w (called conditional Lyapunov exponents) have negative real part. Such conditional Lyapunov exponents can be calculated from the Jacobian matrix Dw H(v(t), w(t)) of the subsystem w calculated around the given chaotic trajectory. In the case of the Chua’s circuits several system decompositions can be taken into account, not all of them lead to a subsystem with conditional Lyapunov exponents with negative real part [Chua et al.