High Order Chua's Circuit and Its FPGA Realization

Author(s):  
Yu Simin ◽  
Lu Jinhu
2013 ◽  
Vol 23 (02) ◽  
pp. 1350022 ◽  
Author(s):  
CHUN HUA WANG ◽  
HAO XU ◽  
FEI YU

A novel approach for constructing a high-order Chua's circuit is proposed. Based on a dual-port RCL network, a high-order Chua's circuit which can generate multi-directional multi-scroll (MDMS) chaotic attractors can be realized by introducing a RC structure and suitable nonlinear functions. First, a fourth-order Chua's circuit is achieved by adding a capacitor, a resistance and a controlled-source constituted by stair functions in the third-order Chua's circuit. And then, this recursive method can be adopted in higher-order Chua's circuit which can generate multi-scroll chaotic attractors in more directions. Finally, a sixth-order Chua's circuit is designed and its experimental results demonstrate the feasibility of this method.


2013 ◽  
Vol 722 ◽  
pp. 33-43
Author(s):  
Zi Long Tang ◽  
Si Min Yu

As an expansion and extension for three-order and four-order Chua's circuit, a new method to construct a class of high-order Chua's circuit and its FPGA hardware implementation has been studied in this paper. Based on the structure of a typical third-order Chua's circuit, a fifth-order, sixth-order and seventh-order Chua's circuit have been constructed through the series in the-type sub-circuit made up by a negative resistance, capacitance, inductance, and resistance, which are stringed into on the inductance slip. The dimensionless equation of high-order Chua's circuit has been, then, derived, and its basic dynamics characteristics have also been analyzed, among which including the phase diagram of chaotic attractors, the dynamic behavior of equilibrium points, bifurcation diagram and the Lyapnuov exponents. Due to digital processing technology, the continuous time state equation of the system has been discretizationed and the state variable ratio transformation has been done, so that the chaotic attractors of high-order Chua's circuit can be generated by using FPGA technology. Taking seventh-order Chua's circuit as a typical example, a general design principle by the way of FPGA technology to generate chaotic attractors as well as the corresponding hardware realization has been presented.


1993 ◽  
Vol 03 (02) ◽  
pp. 645-668 ◽  
Author(s):  
A. N. SHARKOVSKY ◽  
YU. MAISTRENKO ◽  
PH. DEREGEL ◽  
L. O. CHUA

In this paper, we consider an infinite-dimensional extension of Chua's circuit (Fig. 1) obtained by replacing the left portion of the circuit composed of the capacitance C2 and the inductance L by a lossless transmission line as shown in Fig. 2. As we shall see, if the remaining capacitance C1 is equal to zero, the dynamics of this so-called time-delayed Chua's circuit can be reduced to that of a scalar nonlinear difference equation. After deriving the corresponding 1-D map, it will be possible to determine without any approximation the analytical equation of the stability boundaries of cycles of every period n. Since the stability region is nonempty for each n, this proves rigorously that the time-delayed Chua's circuit exhibits the "period-adding" phenomenon where every two consecutive cycles are separated by a chaotic region.


1994 ◽  
Vol 04 (02) ◽  
pp. 117-159 ◽  
Author(s):  
LEON O. CHUA

More than 200 papers, two special issues (Journal of Circuits, Systems, and Computers, March, June, 1993, and IEEE Trans. on Circuits and Systems, vol. 40, no. 10, October, 1993), an International Workshop on Chua’s Circuit: chaotic phenomena and applica tions at NOLTA’93, and a book (edited by R.N. Madan, World Scientific, 1993) on Chua’s circuit have been published since its inception a decade ago. This review paper attempts to present an overview of these timely publications, almost all within the last six months, and to identify four milestones of this very active research area. An important milestone is the recent fabrication of a monolithic Chua’s circuit. The robustness of this IC chip demonstrates that an array of Chua’s circuits can also be fabricated into a monolithic chip, thereby opening the floodgate to many unconventional applications in information technology, synergetics, and even music. The second milestone is the recent global unfolding of Chua’s circuit, obtained by adding a linear resistor in series with the inductor to obtain a canonical Chua’s circuit— now generally referred to as Chua’s oscillator. This circuit is most significant because it is structurally the simplest (it contains only 6 circuit elements) but dynamically the most complex among all nonlinear circuits and systems described by a 21-parameter family of continuous odd-symmetric piecewise-linear vector fields. The third milestone is the recent discovery of several important new phenomena in Chua’s circuits, e.g., stochastic resonance, chaos-chaos type intermittency, 1/f noise spectrum, etc. These new phenomena could have far-reaching theoretical and practical significance. The fourth milestone is the theoretical and experimental demonstration that Chua’s circuit can be easily controlled from a chaotic regime to a prescribed periodic or constant orbit, or it can be synchronized with 2 or more identical Chua’s circuits, operating in an oscillatory, or a chaotic regime. These recent breakthroughs have ushered in a new era where chaos is deliberately created and exploited for unconventional applications, e.g. secure communication.


Sign in / Sign up

Export Citation Format

Share Document