A Chaotic Circuit with Hidden Attractors and Extreme Event

Abstract

Here, a chaotic quadratic oscillator is presented. The chaotic attractor of the oscillator is studied. It has a stable equilibrium point for most of the studied interval of its parameter. So, its chaotic attractor in that interval is hidden. Bifurcation diagrams of the oscillator are studied by changing two parameters. Bifurcations with two initiation methods are plotted for each parameter, and their results are investigated using their corresponding Lyapunov exponents. Studying the bifurcation diagrams reveals the multistability of the oscillator, which is also discussed using the basin of attractions. The existence of extreme events is examined for the chaotic dynamic. Implementing the circuit of the oscillator shows the feasibility of its chaotic dynamics. Author