Survey of Recent Applications of the Chaotic Lozi Map

Abstract

Since its original publication in 1978, Lozi’s chaotic map has been thoroughly explored and continues to be. Hundreds of publications have analyzed its particular structure and applied its properties in many fields (e.g., improvement of physical devices, electrical components such as memristors, cryptography, optimization, evolutionary algorithms, synchronization, control, secure communications, AI with swarm intelligence, chimeras, solitary states, etc.) through algorithms such as the COLM algorithm (Chaotic Optimization algorithm based on Lozi Map), Particle Swarm Optimization (PSO), and Differential Evolution (DE). In this article, we present a survey based on dozens of articles on the use of this map in algorithms aimed at real applications or applications exploring new directions of dynamical systems such as chimeras and solitary states.

Optical voice encryption based on speckle-illuminated fourier ptychography and plaintext-related chaotic random phase mask

“…(1) We achieve plaintext-dependent chaotic random phase masks (CRPMs) by calculating the hash value of the plaintext audio signal using SHA-256 [32] and using the computed hash value to construct the initial values and control parameters for the chaotic Lozi map [33].…”

Dynamical analysis of a new memristive map with offset boosting and extreme multistability

“…In recent years, chaotic systems have received much attention in the fields of communication encryption [22][23][24][25][26], and control optimization [27][28][29], due to the highly complex and unpredictable motion trajectories [30][31][32][33]. Among them, chaotic maps attract the interest of researchers due to the advantages of antijamming, easy numerical simulation, and implementation [34][35][36][37].…”