Generation of a multi-scroll chaotic system via smooth state transformation

The objective of this paper is to generate and analyse a multi-scroll chaotic system from a proposed oscillator system. A novel three-dimensional oscillator system is proposed and analysed for its chaotic range and produces a double-scroll chaotic system. Analogue circuit realization of the proposed oscillator is performed in the Multisim Circuit Design Suite. Further, unlike other nonsmooth methods that involve tedious calculations, a simple and smooth state transformation is proposed which results in multi-scroll attractors of the novel chaotic system. Different qualitative and quantitative tools including time series plot, phase portrait, bifurcation diagram, Lyapunov exponent spectrum, Lyapunov dimension and maximal Lyapunov exponent are used to analyse different behaviours. Simulation is carried out in a MATLAB environment for effective verification of the theoretical approach. The simulation results reveal that the objective is successfully achieved.

Automated summary

The objective of this paper is to generate and analyze a multi-scroll chaotic system from a proposed oscillator system. A novel three-dimensional oscillator system is proposed and analyzed, which produces a double-scroll chaotic system. By using a simple and smooth state transformation, the multi-scroll attractors of the novel chaotic system are obtained.