Cupolet Entanglement Control for Mutual Chaotic Stabilization
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Solution Overview
Problem
Existing techniques fail to effectively stabilize and control unstable periodic orbits in chaotic systems, limiting the ability to achieve entanglement between chaotic systems.
Innovation Solution
The development of cupolet-based control techniques that stabilize chaotic systems onto periodic orbits, allowing for the creation of entangled cupolet pairs through exchange functions, which maintain mutual stabilization and can be extended to multiple chaotic systems.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If conventional control techniques are applied to chaotic systems, then system control is attempted, but the unstable periodic orbits cannot be effectively stabilized
Solution Approach 1:
The patent applies preliminary action by pre-calculating and storing optimal control sequences for stabilizing specific unstable periodic orbits (UPOs) in chaotic systems. These pre-computed control sequences are then retrieved and applied when stabilization is needed, avoiding the complexity of real-time computation and achieving reliable stabilization of periodic orbits.
Solution Approach 2:
The patent introduces an intermediary mechanism (control sequence generator and lookup table) that mediates between the chaotic system and the stabilization goal. The intermediary pre-processes the control information and stores it in a structured format, making the stabilization process more reliable and less sensitive to initial conditions.
2Adaptability or versatility
If entanglement between chaotic systems is achieved using cupolet pairs, then correlated relationship is established, but system complexity increases
Solution Approach 1:
The patent uses copying by creating identical or mirrored chaotic systems (copies) that can be entangled through cupolet pairs. Each system is controlled to stabilize on corresponding UPOs, and their visitation sequences are exchanged to establish entanglement. This copying approach enables entanglement capability while keeping individual system structures relatively simple.
Solution Approach 2:
The patent implements universality by designing a general-purpose entanglement framework that can be applied to different types of chaotic systems. The cupolet-based control mechanism and visitation sequence exchange protocol are universal methods that work across various chaotic system configurations, enabling adaptable entanglement without requiring system-specific complex designs.
3Reliability
If visitation sequences are exchanged between chaotic systems to maintain entanglement, then mutual stabilization is achieved, but control complexity increases
Solution Approach 1:
The patent applies feedback by continuously monitoring the visitation sequences of entangled chaotic systems and using this information to adjust control inputs. The exchanged visitation sequences serve as feedback signals that indicate the current state of each system, allowing the control mechanism to maintain mutual stabilization by making real-time adjustments based on the observed dynamics.
Solution Approach 2:
The patent implements self-service by designing the entangled chaotic systems to mutually provide control information through visitation sequence exchange. Each system's natural dynamics generate the visitation sequence that serves as control input for the other system, reducing the need for external complex control mechanisms while maintaining reliable mutual stabilization.
Data Source
AI summary
Systems, methods, apparatus, and techniques are presented for maintaining cupolets in a state of mutual stabilization. A first cupolet and a second cupolet are generated. A first control code is applied to the first cupolet for a first time to produce a first visitation code. The first visitation code is transformed based on an exchange function to produce a second control code. The second control code is applied to the second cupolet to produce a second visitation code. The second visitation code is transformed based on the exchange function to produce the first control code. The first control code is applied to the first cupolet for a second time.