A Novel Approach to Structured Multistability in a 3D Chaotic System: Implementation and Circuit Validation

ABSTRACT This study presents a new three‐dimensional chaotic system characterized by a solitary unstable equilibrium point and introduces the direct derivative integration (DDI) approach for attaining accurate control of multistable dynamics. The direct derivative integration (DDI) method expands the 3D seed system into a six‐dimensional framework by incorporating its derivatives, maintaining the inherent chaotic behavior, but facilitating ongoing offset enhancement to create a structured lattice of coexisting attractors. A physical implementation of the system was executed using a breadboard prototype to validate the theoretical study, with findings corroborated by circuit simulations. The results indicate that the suggested method successfully produces an unlimited array of coexisting attractors organized in a structured grid, underscoring the practical viability and dependability of the direct derivative integration (DDI) approach for the creation of chaotic systems with manageable multistability.

• three-dimensional chaotic system
• multistability
• coexisting attractors
• unstable equilibrium
• chaotic circuits
• breadboard prototype

• Chaos control and synchronization
• Chaos-based Image/Signal Encryption
• Mathematical Dynamics and Fractals
• three-dimensional chaotic system
• multistability
• coexisting attractors
• unstable equilibrium
• chaotic circuits
• breadboard prototype
• Statistical and Nonlinear Physics
• Computer Vision and Pattern Recognition
• Mathematical Physics
• Physics and Astronomy
• Computer Science
• Mathematics