A New Chaotic System with Multiple Attractors: Dynamic Analysis, Circuit Realization and S-Box Design

Area of Science:

• Nonlinear Dynamics
• Chaos Theory
• Cryptography

Background:

• Chaotic systems are crucial for generating complex, unpredictable behavior.
• Understanding multi-stability and coexisting attractors is key in nonlinear dynamics.
• Secure cryptographic systems require robust, complex signal generation.

Purpose of the Study:

• To introduce a novel three-dimensional chaotic system with unique dynamic properties.
• To explore the system's complex behaviors, including multiple attractors and coexisting states.
• To develop and evaluate a new S-Box for cryptographic applications based on the proposed chaotic system.

Main Methods:

• Analysis of system equilibria for different parameter values.
• Numerical simulations to reveal complex dynamic behaviors.
• Design and performance testing of a novel S-Box for cryptography.

Main Results:

• The novel system exhibits multiple equilibria, including stable, saddle node, and saddle foci.
• The system demonstrates rich dynamics: mono-stability, bi-stability, periodicity, and coexisting strange attractors.
• A new S-Box was developed, showing competitive performance compared to existing designs.

Conclusions:

• The proposed 3D chaotic system offers a rich platform for studying complex dynamics and multi-stability.
• The developed S-Box shows potential for enhancing cryptographic security.
• This work bridges nonlinear dynamics with practical cryptographic applications.