Inductor-free simplified Chua’s circuit only using two-op-amp-based realization

Abstract

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.