Adaptive Synchronization Strategy between Two Autonomous Dissipative Chaotic Systems Using Fractional-Order
Licai Liu1, Chuanhong Du1, Xiefu Zhang2
1School of Electronic and Information Engineering, Anshun University, Anshun 561000, China.
Entropy (Basel, Switzerland)
|December 3, 2020
Summary
This study introduces two novel four-dimensional chaotic systems, enhancing complexity beyond lower-dimensional models. An adaptive synchronization method is presented for these fractional-order chaotic systems, proving reliable for diverse parameter conditions.
Area of Science:
- Nonlinear Dynamics and Chaos Theory
- Control Systems Engineering
- Fractional Calculus Applications
Background:
- Fractional-order chaotic systems offer higher complexity compared to low-dimensional integer-order systems.
- Synchronization of fractional-order chaotic systems is challenging, often requiring complex control functions.
- Existing methods may not adequately address synchronization under uncertain parameters.
Purpose of the Study:
- To introduce and analyze two novel four-dimensional, continuous, autonomous, and dissipative fractional-order chaotic system models.
- To develop and validate an adaptive, large-scale, asymptotic synchronization control method for fractional-order chaotic systems.
- To demonstrate the synchronization of two distinct fractional-order chaotic systems, even with unknown parameters.
Main Methods:
- Numerical simulations were employed to verify the rich dynamic behaviors of the proposed four-dimensional chaotic systems.
- Fractional Mittag-Leffler stability theory was utilized as the foundation for designing the adaptive synchronization controller.
- An adaptive control scheme was developed to achieve asymptotic synchronization between different fractional-order chaotic systems.
Main Results:
- The two novel four-dimensional fractional-order chaotic systems exhibit complex and rich dynamic behaviors.
- The proposed adaptive synchronization control method successfully achieves asymptotic synchronization for fractional-order chaotic systems.
- The controller demonstrates reliability in synchronizing systems with both known and uncertain parameters.
Conclusions:
- The developed adaptive synchronization scheme provides a reliable method for controlling fractional-order chaotic systems.
- This research contributes to the theoretical understanding and practical engineering applications of chaos synchronization.
- The findings pave the way for advanced applications in areas requiring complex system dynamics and control.
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