Chaos in a second-order non-autonomous Wien-bridge oscillator without extra nonlinearity

Abstract

Purpose

The purpose of this paper is to develop a simple chaotic circuit. The circuit can be fabricated by less discrete electronic components, within which complex dynamical behaviors can be generated.

Design/methodology/approach

A second-order non-autonomous inductor-free chaotic circuit is presented, which is obtained by introducing a sinusoidal voltage stimulus into the classical Wien-bridge oscillator. The proposed circuit only has two dynamic elements, and its nonlinearity is realized by the saturation characteristic of the operational amplifier in the classical Wien-bridge oscillator. After that, its dynamical behaviors are revealed by means of bifurcation diagram, Lyapunov exponent and phase portrait and further confirmed using the 0-1 test method. Moreover, an analog circuit using less discrete electronic components is implemented, and its experimental results are measured to verify the numerical simulations.

Findings

The equilibrium point located in a line segment varies with time evolution, which leads to the occurrence of periodic, quasi-periodic and chaotic behaviors in the proposed circuit.

Originality/value

Unlike the previously published works, the significant values of the proposed circuit with simple topology are inductor-free realization and without extra nonlinearity, which make the circuit can be used as a paradigm for academic teaching and experimental illustraction for chaos.

Citation

Xu, Q., Zhang, Q., Jiang, T., Bao, B. and Chen, M. (2018), "Chaos in a second-order non-autonomous Wien-bridge oscillator without extra nonlinearity", Circuit World, Vol. 44 No. 3, pp. 108-114. https://doi.org/10.1108/CW-11-2017-0063