Exponential Stability of Impulsive Stochastic Delay System Based on Razumikhin Method and Its Application to Chaos Control

In this paper, the exponential stability of a stochastic delay system with impulsive signal is considered, and stability theorem of this system is proposed based on the Lyapunov–Razumikhin method; the convergence rate is also given, which gives theoretical foundation to chaos control and synchronization using the impulsive method. Finally, the classic delay chaos system with white noise and impulsive signal is employed to verify the feasibility and effectiveness of our theorem.

Configurational Entropy for Optimizing the Encryption of Digital Elevation Model Based on Chaos System and Linear Prediction

A digital elevation model (DEM) digitally records information about terrain variations and has found many applications in different fields of geosciences. To protect such digital information, encryption is one technique. Numerous encryption algorithms have been developed and can be used for DEM. A good encryption algorithm should change both the compositional and configurational information of a DEM in the encryption process. However, current methods do not fully take into full consideration pixel structures when measuring the complexity of an encrypted DEM (e.g., using Shannon entropy and correlation). Therefore, this study first proposes that configurational entropy capturing both compositional and configurational information can be used to optimize encryption from the perspective of the Second Law of Thermodynamics. Subsequently, an encryption algorithm based on the integration of the chaos system and linear prediction is designed, where the one with the maximum absolute configurational entropy difference compared to the original DEM is selected. Two experimental DEMs are encrypted for 10 times. The experimental results and security analysis show that the proposed algorithm is effective and that configurational entropy can help optimize the encryption and can provide guidelines for evaluating the encrypted DEM.