A novel hyperchaotic system with fast and slow attractors

Abstract

A novel hyperchaotic system with only one equilibrium point is proposed by introducing an additional state feedback. The dynamic behaviors of this system are investigated by means of the Lyapunov exponent, Poincaré map, and bifurcation diagrams, i.e., this new hyperchaotic system possesses two positive Lyapunov exponents within a large range. Interestingly, the chaotic attractor of the system is special with two slow and fast attractors, that is, the system is a combination of slow and fast parts. The bound estimation of this system is also investigated. In addition, the image cryptology method is performed. In the image encryption part, an algorithm is suggested to provide confusion and diffusion operations on the image. The results show that, by employing the hyperchaotic system, the original image information can be completely hidden after being encrypted and can be decrypted efficiently.