Single amplifier biquad based inductor-free Chua’s circuit

Abstract

The present paper reports an inductor-free realization of Chua's circuit, which is designed by suitably cascading a single amplifier biquad based active band pass filter with a Chua's diode. The system has been mathematically modeled with three-coupled firstorder autonomous nonlinear differential equations. It has been shown through numerical simulations of the mathematical model and hardware experiments, that the circuit emulates the behaviors of a classical Chua's circuit, e.g., fixed point behavior, limit cycle oscillation, period doubling cascade, chaotic spiral attractors, chaotic double scrolls and boundary crisis. The occurrence of chaotic oscillation has been established through experimental power spectrum, and quantified with the dynamical measure like Lyapunov exponents.

An Improved Memristive Diode Bridge‐Based Band Pass Filter Chaotic Circuit

“…A second-order active BPF circuit has a simple circuit topology, which contains only one amplifier, two capacitors, and four resistors [40]. In this paper, by replacing a series resistor with the proposed memristive diode bridge emulator, a third-order memristive BPF circuit is proposed, as shown in Figure 1(b).…”

Design of Chaotic and Hyperchaotic Time-Delayed Electronic Circuit

“…Apart from the mathematical modeling of the naturally occurring phenomena, nonlinear delay dynamical systems have been extensively studied in the literature, and several new systems were proposed [8,9] due to the following reasons: (i) owing to the infinite dimensionality, DDEs shows higher dimensional chaotic behavior that cannot be anticipated by a low dimensional system [10]. Understanding and exploring the behavior of these systems are important both from the academic and engineering perspectives, (ii) infinite dimensionality of delayed systems offers a great opportunity to the researchers to harness the richness of hyperchaos, having multiple positive Lyapunov exponents (LEs).…”

The Negative Side of Chua's Circuit Parameter Space: Stability Analysis, Period-Adding, Basin of Attraction Metamorphoses, and Experimental Investigation

“…In this system, domains of periodicity immersed in chaotic regions of 2D parameter space are organized in period-adding cascades with spiral configurations along homoclinic bifurcations [Komuro et al, 1991;Albuquerque & Rech, 2012]. Moreover, the implementation of Chua's circuit is easy and allows to perform experiments whose results present great agreement with computational simulations [Matsumoto et al, 1985;Zhong & Ayrom, 1985;Weldon, 1990;Cruz & Chua, 1992;Kennedy, 1992;Cruz & Chua, 1993;Rodriguez-Vazquez & Delgado-Restituto, 1993;Morgül, 1995;Senani & Gupta, 1998;Elwakil & Kennedy, 2000;Tôrres & Aguirre, R. O. Medrano-T & R. Rocha 2000;Kiliç et al, 2002;Barboza, 2008;Rocha & Medrano-T, 2009;Trejo-Guerra et al, 2010;Rocha et al, 2010;Banerjee, 2012].…”