By Luigi Fortuna, Mattia Frasca, Maria Gabriella Xibilia
Because the start of the Chua circuit in 1983, numerous fruitful, attention-grabbing and proper learn subject matters have arisen. In honor of the twenty fifth anniversary of the discovery of Chua's circuit, this ebook provides the 25 years of study at the implementation of Chua's circuit, and in addition discusses destiny instructions and rising purposes 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 issues and complex effects which have been lately bought. With approximately 60 illustrations incorporated within the e-book, it additionally exhibits the designated schematics of numerous diversified implementations that may be simply reproduced with a inexpensive experimental setup and PC-based size instrumentation. Contents: The delivery 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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Extra info for Chua's circuit implementations: yesterday, today, and tomorrow
28 Projection of the attractor of the hyperchaotic Chua’s circuit into the plane x − w (a) and y − z (b). Further generalizations to higher dimensions are dealt with in [Lukin (1993); Sharkovsky et al. (1993)], where the RLC subcircuit is substituted by a coaxial cable or by a lossless transmission line. Finally, many works have investigated higher order systems made of elementary units which are Chua’s circuits. Among those works, we mention studies on one- or two-dimensional arrays of Chua’s circuits [Perez-Munuzuri et al.
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 + . Another closed loop method that can be applied to control the Chua’s technique is the Pyragas’ technique [Pyragas (1992); Pyragas and Tamasevicius (1993); Pyragas (1995, 2006)], in which a time-delayed feedback of the state variables is used to stabilize the unstable periodic orbits of the strange attractor.
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.