Dynamics analysis of a four-dimensional hyperchaotic hidden system and its application in image encryption

Area of Science:

• Nonlinear Dynamics and Chaos Theory
• Complex Systems Research
• Higher-Dimensional Chaotic Systems

Background:

• Traditional chaotic systems often lack equilibria or exhibit limited complexity.
• Exploring higher-dimensional chaotic systems is crucial for understanding complex phenomena.
• Hidden attractors present unique challenges and opportunities in dynamical systems research.

Purpose of the Study:

• To propose a novel four-dimensional hyperchaotic system with hidden attractors.
• To investigate the complex dynamic behaviors and multistability of the proposed system.
• To validate the system's practical applicability through circuit implementation and image encryption.

Main Methods:

• Development of a four-dimensional quadratic chaotic flow.
• Nonlinear dynamical analysis to explore system behaviors and multistability.
• Analog circuit simulation using Multisim 14.0 for validation.
• Image encryption utilizing DNA encoding and chaotic sequences for diffusion.

Main Results:

• The proposed system exhibits complex dynamics and possesses multiple hidden attractors, demonstrating multistability.
• Circuit simulation successfully validates the system's behavior.
• The image encryption algorithm shows effective diffusion and robustness, analyzed via histograms, information entropy, and correlation.

Conclusions:

• The novel four-dimensional hyperchaotic system expands the scope of chaos theory research.
• The system's multistability and complex dynamics are confirmed through theoretical analysis and simulation.
• The proposed image encryption algorithm is effective and resilient against common attacks, highlighting the practical utility of the chaotic system.