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Bifurcation and Chaos
Published in Wai-Kai Chen, Feedback, Nonlinear, and Distributed Circuits, 2018
Michael Peter Kennedy, Vandenberghe Lieven
Chua’s oscillator [5] (see Figure 14.26) is derived from Chua’s circuit by adding a resistor R0 in series with the inductor L. The oscillator contains a linear inductor, two linear resistors, two linear capacitors, and a single Chua diode NR. NR is a voltage-controlled piecewise-linear resistor whose continuous odd-symmetric three-segment DP characteristic (see Figure 14.18) is described explicitly by the relationship IR=GbVR+12(Ga−Gb)(|VR+E|−|VR−E|)
Strange attractors and continuous-time chaotic systems
Published in Arturo Buscarino, Luigi Fortuna, Mattia Frasca, ®and Laboratory Experiments, 2017
Arturo Buscarino, Luigi Fortuna, Mattia Frasca
With reference to the piecewise-linear form of the nonlinearity, the mechanism underlying the birth of chaos in the Chua’s circuit is based on a balance between the behavior in the different regions defined by the slopes of the nonlinearity. When the circuit works in the region with a negative slope, the Chua’s diode provides energy to the passive network, so that oscillations are amplified. This will move the system towards one of the regions with positive slope (positive resistance), where the system is passive and oscillations are damped out, so that it returns back to the region of negative resistance and so on.
Fractals and chaos
Published in A. W. Jayawardena, Environmental and Hydrological Systems Modelling, 2013
Chua’s circuit (Chua and Lin, 1990) is the simplest electronic circuit that exhibit chaos. It is a parallel LRC5 circuit consisting of two linear capacitors, one linear inductor, two linear resistors, and a non-linear resistor (referred to as Chua’s diode). The set of equations that relates the voltages across the two capacitors, according to Kirchoff’s laws, take the form () C1dV1dt=1R(V2−V1)−f(V1) () C2dV2dt=−1R(V2−V1)+I () LdIdt=−rI−V2
Identification of Chua’s chaotic circuit parameters using penguins search optimisation algorithm
Published in Cyber-Physical Systems, 2022
Fouzia Maamri, Sofiane Bououden, Ilyes Boulkaibet
Chua circuit is a type of electronic circuit invented by Leon Chua in 1983, where this circuit generates a wide variety of chaos and bifurcation phenomena [35,36]. Chua’s circuit can be considered as a very simple deterministic and powerful system that defines chaotic requirements [37]. This circuit received a great deal of attention in the study of complex nonlinear dynamical phenomena and has been an important example in the study of chaos, bifurcation and fractal geometry [38]. The output of Chua’s circuit is not predictable, and it can be used for signal processing, encrypt data, secure communication, and produces an oscillating waveform [1]. Chua’s circuit may exhibit a wide variety of nonlinear behaviours, and it has become an attractive paradigm for the experimental investigation of chaotic dynamical systems [35].
Asymmetric memristive Chua’s chaotic circuits
Published in International Journal of Electronics, 2021
Mengjie Hua, Huagan Wu, Quan Xu, Mo Chen, Bocheng Bao
Only using a simple nonlinear resistor of Chua’s diode, Chua’s circuit is a classical analog electronic circuit exhibiting chaos. It possesses three unstable equilibrium points consisting of one zero saddle point and two symmetric nonzero saddle-foci, leading to the emergence of symmetric double-scroll chaotic attractor (Fortuna et al., 2009). For the hardware implementation of Chua’s circuit, the main concern is with circuitry to implement the Chua’s diode. By employing two-stage op-amp-based negative impedance converters (NICs) (Kennedy, 1992), two transistors (Matsumoto et al., 1986), active diode pair (Bao, Wu et al., 2018), one-stage op-amp-based NIC (Bao, Li et al., 2016), three-stage op-amp-based NICs (Bao, Jiang et al., 2016), simplified multi-segment piecewise-linear resistors (Wang, Li et al., 2019), and memristive diode-bridge emulator (Chen et al., 2015), numerous implementations of Chua’s diode were reported in the past three decades. Particularly, these circuit-implemented Chua’s diodes can achieve various symmetric voltage-current characteristics and their specific nonlinearities cause the Chua’s circuit to exhibit self-excited or hidden chaotic attractors with different symmetric topological structures.
Fault estimation and controller compensation in Lure systems by LPV-embedding
Published in International Journal of Control, 2019
Ainain Nur Hanafi, Maria M. Seron, José A. De Doná
In this section, the FTC strategies presented in Sections 4–6 are demonstrated for the Chua circuit shown in Figure 2. The Chua circuit produces a chaotic behaviour by combining a nonlinear active resistance and energy storage elements. The dynamics of the system are given by where is the (scaled) voltage-controlled current source, f is the magnitude of a possible actuator fault and is the bounded input disturbance. The states x1, x2, x3 represent the voltage across capacitor C1, the voltage across capacitor C2 and the current through inductor L, respectively. R0 and R are linear resistors, and α1 = 1/(RC1), α2 = 1/(RC2) and α3 = 1/L are scalar parameters. The term g(x1) is a piecewise-linear function defined by and plotted in Figure 3.