A Conservative Chaotic Oscillator: Dynamical Analysis and Circuit Implementation

Abstract

This paper introduces a new 3D conservative chaotic system. The oscillator preserves the energy over time, according to the Kaplan–Yorke dimension computation. It has a line of unstable equilibrium points that are investigated with the help of eigenvalues and also numerical analysis. The bifurcation diagrams and the corresponding Lyapunov exponents show various behaviors, for example, chaos, limit cycle, and torus with different parameters. Other dynamical properties, such as Poincaré section and basin of attraction, are investigated. Additionally, an oscillator’s electrical circuit is designed and implemented to demonstrate its potentiality.