Ghost attractor in fractional order blinking system and its application

Abstract

In this paper, the occurrence of ghost attractor is verified in three cases of a proposed fractional order Rössler blinking system. Firstly, the dynamical behaviors of the short memory fractional order prototype-4 Rössler system with Chua’s diode are explored via bifurcation diagrams and Lyapunov exponents. It is depicted that this system exhibits a variety of dynamics including limit cycles, period doubling and chaos. Then, a proposed non-autonomous fractional order Rössler blinking system is introduced. Numerical simulations are employed to confirm the existence of ghost attractors at specific cases which involve very fast switching time between two composing autonomous fractional subsystems. It is found that the presented fractional order blinking system is very sensitive to system parameters, initial conditions, and stochastic process parameters. Thus, the induced chaotic ghost attractor is utilized in a suggested ghost attractor-based chaotic image encryption scheme for first time. Finally, a detailed security analysis is carried out and reveals that the proposed image cryptosystem is immune against different types of attacks such as differential attacks, brute force attacks, cropping and statistical attacks.