Affiliation:
1. LJAD, CNRS, Université Côte d’Azur, F-06000 Nice, France
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.
Subject
Computational Mathematics,Computational Theory and Mathematics,Numerical Analysis,Theoretical Computer Science
Reference167 articles.
1. Zeraoulia, E. (2013). Lozi Mappings—Theory and Applications, CRC Press.
2. Coexistence of Thread and Sheet Chaotic Attractors for Three-Dimensional Lozi Map;Lozi;Dynamics,2023
3. Dynamical systems with turbulent behavior;Doplicher;Mathematical Problems in Theoretical Physics,1978
4. Some elements for a history of the dynamical systems theory;Letellier;Chaos,2021
5. Deterministic nonperiodic flow;Lorenz;J. Atmos. Sci.,1963