A Novel Chaotic System With Boomerang-Shaped Equilibrium, Its Circuit Implementation and Application to Sound Encryption

Abstract

In the chaos literature, there has been much attention paid to chaotic systems with uncountable equilibrium points such as systems with line equilibrium, curve equilibrium. This paper reports a 3-D chaotic system with a closed curve of equilibrium points, which has the shape of a boomerang. Dynamics of the chaotic system with the boomerang equilibrium has been studied by using phase portraits, bifurcation diagram, Lyapunov exponents and Lyapunov dimension. Also, we design an electronic circuit implementation of the theoretical system to check its feasibility. As an application of the new chaotic system, we have derived new results for sound encryption with the new chaotic system.