By Luigi Fortuna, Mattia Frasca, Maria Gabriella Xibilia
Because the start of the Chua circuit in 1983, a variety of fruitful, interesting and suitable learn themes have arisen. In honor of the twenty fifth anniversary of the discovery of Chua's circuit, this publication offers the 25 years of analysis at the implementation of Chua's circuit, and likewise discusses destiny instructions and rising purposes of modern effects. the aim of the ebook is to supply researchers, PhD scholars, and undergraduate scholars a study monograph containing either basics at the subject matters and complicated effects which were lately received. With approximately 60 illustrations incorporated within the ebook, it additionally exhibits the certain 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 purposes of Chua's Circuit
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Extra resources for Chua's circuit implementations: yesterday, today, and tomorrow
This mechanism causes the typical trajectory to rotate around P + or − P for a certain time and then to go back to the equilibrium or be pushed towards the other in an irregular way and accounts for the sensitive dependence on initial conditions. Two trajectories starting from two very close points in D1 may evolve in a complete diﬀerent manner depending on where circuit February 10, 2009 17:2 World Scientific Book - 9in x 6in The birth of the Chua’s circuit circuit 21 they will cross the plane U1 .
Attractors which have a fractal geometry but nonpositive Lyapunov exponents [Grebogi et al. (1984)]. Fig. 2 The Murali-Lakshmanan-Chua circuit [Murali et al. (1994b)]. Hyperchaos in the Chua’s circuit The Chua’s circuit can also generate hyperchaotic behavior. 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.
Such techniques to couple two or more chaotic circuits can be mainly divided into two classes: drive-response (or unidirectional) coupling and bidirectional coupling. In the ﬁrst case, one circuit drives another one called the response (or slave) system, while on the contrary in bidirectional coupling February 10, 2009 52 17:2 World Scientific Book - 9in x 6in circuit Chua’s circuit implementations: yesterday, today and tomorrow both the circuits are connected and each circuit inﬂuences the dynamics of the other.