Discrete mathematics

Physics

Nonlinear system

Bifurcation

Mathematics

Bifurcation diagram

Countable set

Statistical physics

Phase portrait

Mathematical analysis

Uncountable set

Encryption

Artificial intelligence

Control (management)

Lyapunov exponent

Chaotic

Computer science

Quantum mechanics

Differential equation

Equilibrium point

Computer security

Control theory (sociology)

Iranian Journal of Science and Technology Transactions of Electrical Engineering

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.

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