Construction of multi-state chaotic systems and applications to image encryption

This paper presents a novel method for constructing chaotic systems based on state variables and small parameters, demonstrating its universal applicability and exploring its implementation in image encryption. First, a new chaotic system is constructed by combining state variables and small parameters, and the influence of system parameters on its dynamic behavior is analyzed in detail by combining the classic Lorenz chaotic system. To further enhance the system design, memristors are incorporated alongside state variables and small parameters, resulting in an innovative approach for constructing multi-wing attractor chaotic systems. The generation mechanisms and dynamic characteristics of these attractors are systematically investigated by varying initial conditions. Moreover, the proposed construction method is extended to fractional-order systems to verify its feasibility, with the system's dynamic behavior analyzed using the SALI algorithm. The universal applicability of this method is validated through both the T-system and Liu-system cases. Building upon the improved chaotic system, a multi-state chaotic image encryption algorithm is developed, forming a comprehensive encryption framework. The security and robustness of the proposed system are rigorously evaluated through histogram analysis, information entropy calculations, and plaintext sensitivity tests. The findings provide a solid theoretical foundation and practical guidance for applying multi-state chaotic systems in secure image encryption, demonstrating significant potential for enhancing encryption performance.