A delay coupling method to reduce the dynamical degradation of digital chaotic maps and its application for image encryption

In this study, a novel delayed coupled chaotic model to reduce the dynamical degradation of digital chaotic maps is firstly proposed. In this model, we introduce the delayed state variables in digital maps and use the state variable of one map to vary the control parameter of the other map. Numerical experimental results demonstrate that the delayed coupled system can effectively reduce the dynamical degradation of digital chaotic maps, and retain the phase space structure of the original system. Furthermore, we propose a simple image encryption algorithm based on the coupled model as a simple application. Numerical experiments show that our algorithm has high security level and can resist various attacks, which is competitive with some other chaotic image encryption algorithms.