Inductor-free simplified Chua’s circuit only using two-op-amp-based realization
- 336 Downloads
Based on a classical Wien bridge oscillator and a simplified Chua’s diode only using one op-amp realization, an inductor-free simplified Chua’s circuit is presented in this paper. The newly proposed circuit has only two op-amps, three capacitors, and eight resistors and, to our knowledge, is a simplest inductor-free Chua’s circuit. The state equations and their dimensionless equations are mathematically modeled. Through numerical simulations of the mathematical model and hardware experiments, the circuit emulates the dynamical behaviors of a classical Chua’s circuit, e.g., coexisting limit cycle oscillations, limit cycle oscillations, period doubling cascades, coexisting chaotic spiral attractors, chaotic double scrolls and boundary crisis. However, different from the classical Chua’s circuit, the inductor-free simplified Chua’s circuit is divided into a non-dissipative region and two dissipative regions in whole state space, resulting in the occurrence of the hollow double-scroll chaotic attractor. Furthermore, an active band pass filter-based inductor-free simplified Chua’s circuit is extended, and numerical simulations and hardware experiments are performed, from which similar dynamical behaviors are exhibited.
KeywordsChaos Chua’s circuit Realization Op-amp Wien bridge oscillator Active band pass filter
This work was supported by the grants from the National Natural Science Foundations of China (Grant No. 51277017) and the Natural Science Foundations of Changzhou, Jiangsu Province, China (Grant No. CJ20159026).
- 1.Fortuna, L., Frasca, M., Xibilia, M.G.: Chua’s Circuit Implementations: Yesterday, Today and Tomorrow. World Scientific, Singapore (2009)Google Scholar
- 2.Kiliç, R.: A practical guide for studying Chua’s circuits. World Scientific, Singapore (2010)Google Scholar
- 14.Xi, F., Chen, S.Y., Liu, Z.: Chaotic analog-to-information conversion: principle and reconstructability with parameter identifiability. Int. J. Bifurc. Chaos 23(9), 1430025-1–1430025-17 (2014)Google Scholar
- 17.Chen, M., Yu, J.J., Bao, B.C.: Finding hidden attractors in improved memristor-based Chua’s circuit. Electron. Lett. 51(6), 462–464 (2015)Google Scholar
- 28.Kiliç, R., Yildirim, F.: A survey of Wien bridge-based chaotic oscillators: design and experimental issues. Chaos Solitons Fractals 38(5), 1394–1410 (2008)Google Scholar
- 29.Yu, Q., Bao, B.C., Hu, F.W., Xu, Q., Chen, M., Wang, J.: Wien-bridge chaotic oscillator based on first-order generalized memristor. Acta Phys. Sin. 63(24), 240505-1–240505-14 (2014)Google Scholar
- 30.Rizwana, R., Mohamed, I.R.: Investigation of chaotic and strange nonchaotic phenomena in nonautonomous Wien-bridge oscillator with diode nonlinearity. J. Nonlinear Dyn. 2015, 612516-1–612516-7 (2015)Google Scholar