Oscillator without equilibrium and linear terms: Dynamics and application

Abstract

A significant attention has concentrated on systems with “hidden attractors” in recent years. The aim of this work is to study an oscillator displaying “hidden attractors”. The oscillator has all nonlinear terms but no equilibrium. The oscillator exhibits attractive dynamics such as chaos, bubble bifurcation, symmetrical attractors, and boosting attractors. Oscillator's feasibility is verified by a microcontroller. Utilizing the oscillator for biomedical image encryption illustrates its application. In addition, the adaptive control is designed for the oscillator.

Keywords

• Chaotic system
• Hidden attractor
• Microcontroller
• Equilibrium
• Encryption