Infinitely many coexisting conservative flows in a 4D conservative system inspired by LC circuit

Abstract

Conservative chaotic flows, a category of incompressible chaos, are usually generated from dynamical systems without dissipation. The existing results on conservative chaos are almost reported in mathematical models of coupled ordinary differential equations, but rarely raised in circuit models. This paper proposes a four-dimensional conservative chaotic system inspired by inductor–capacitor (LC) circuit. It is implemented by replacing two RC networks in Wien bridge oscillator with two LC networks. The circuit has only one piecewise nonlinearity featured by the saturation output characteristic of operational amplifier and is likely to be the simplest such model. With dimensionless equations, the conservative nature of the system is analysed. Both theoretical analyses and numerical simulations confirm the system is conservative. Particularly, with fixed system parameters, infinitely many coexisting periodic, quasiperiodic and chaotic flows are observed. The PSIM circuit simulations and DSP-based hardware experiments demonstrate the findings. Finally, pseudorandom number generator based on the conservative chaotic system is designed to generate high-quality pseudorandom bits.