Chaotic system generator based on meta-heuristic optimization algorithms

Chaotic systems have an important role in many disciplines, particularly in computer science, due to their unpredictable dynamic behavior despite being deterministic. Especially one-dimensional chaotic maps, which stand out with their low computational cost and simple structure, are widely preferred in applications. However, despite these advantages, they may have weaknesses such as short chaotic range and limited dynamic behavior. Therefore, improving on existing maps or proposing new one-dimensional chaotic maps with better chaotic behavior contributes to the development of powerful methods. In this thesis, an architecture is proposed for the discovery of new one-dimensional chaotic maps, which involves a complex and demanding process. The architecture developed by using meta-heuristic optimization method has the flexibility to generate chaotic maps for diverse structural properties and application purposes. In the experiments conducted in the study, new one-dimensional chaotic maps were obtained by applying four different scenarios for the proposed architecture and evaluated with various analysis methods. The experimental results show that the proposed architecture is capable of generating maps exhibiting rich dynamic behavior, large chaotic regions, strong ergodicity and high statistical randomness. One of the most remarkable aspects of this work, which differs from similar works in the literature, is that a wide variety of chaotic maps can be generated by heuristically selecting components from a vast functional and mathematical term space without being restricted to limited and fixed structures. This flexibility not only provides a wider variety in terms of theoretical analysis but also enables the design of customized chaotic systems in applications. All findings show that the proposed approach offers a more flexible, optimizable and powerful framework for applications compared to existing methods in the literature and has high potential especially in areas such as cryptography and random number generation. This study aims to make a significant contribution to the body of knowledge in the field of chaos theory and applications by designing new chaotic maps and demonstrating their usability.