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Special Characteristics and Synchronizations of Multi Hybrid-Order Chaotic Systems
Jiaxun Liu1, Zuoxun Wang1, Fangfang Zhang1,2,3
1School of Electrical Engineering and Automation, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China.
Entropy (Basel, Switzerland)
|December 8, 2020
Summary
This study introduces hybrid chaotic systems combining integer and fractional orders, defining key concepts like hybrid degree (HD). Researchers achieved combination synchronization for these novel systems, verifying controller effectiveness.
Area of Science:
- Chaos theory
- Nonlinear dynamics
- Fractional calculus
Background:
- Integer and fractional chaotic systems offer unique advantages.
- A need exists for unified frameworks to explore their combined properties.
- Existing research lacks comprehensive definitions for hybrid chaotic systems.
Purpose of the Study:
- To propose definitions and fundamental concepts for hybrid chaotic systems.
- To investigate the properties of hybrid Lorenz and classic chaotic systems.
- To establish relationships between hybrid degree (HD), lowest order (LO), and total dimension order (TDO).
Main Methods:
- Definition of hybrid chaotic systems and associated concepts (HD, LO, TDO).
- Analysis of preliminary properties of hybrid Lorenz systems and other classic systems.
- Investigation of the relationship between HD, LO, TDO, and system parameters.
- Application of incommensurate fractional stability theory for synchronization.
Main Results:
- Novel definitions for hybrid chaotic systems, including HD, LO, and TDO, are proposed.
- Preliminary properties of hybrid Lorenz systems and other chaotic systems were studied.
- The relationship between HD (linked to fractional order) and LO/TDO was investigated.
- Combination synchronization was achieved for three distinct hybrid order chaotic systems.
Conclusions:
- Hybrid chaotic systems offer a promising framework for exploring complex dynamics.
- The proposed concepts (HD, LO, TDO) provide a structured approach to analyzing these systems.
- The developed synchronization controller is effective for hybrid order chaotic systems.
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