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Synchronization of Fractional-Order Complex Chaotic Systems Based on Observers
Zhonghui Li1, Tongshui Xia1, Cuimei Jiang2
1Business School, Shandong Normal University, Jinan 250014, China.
Entropy (Basel, Switzerland)
|December 3, 2020
Summary
Researchers developed complex modified projective synchronization for nonlinear fractional-order complex chaotic systems. This effective method, applicable to various chaotic systems, ensures stability and enables synchronization for engineering applications.
Area of Science:
- Nonlinear dynamics
- Chaos theory
- Fractional-order systems
Background:
- Fractional-order chaotic systems exhibit complex dynamics.
- Synchronization of chaotic systems is crucial for secure communication and signal processing.
- Existing synchronization methods may not be universally applicable to all fractional-order chaotic systems.
Purpose of the Study:
- To investigate a new synchronization technique called complex modified projective synchronization.
- To develop a state observer-based method for achieving this synchronization in nonlinear fractional-order complex chaotic systems.
- To demonstrate the broad applicability of the proposed method to diverse fractional-order chaotic systems.
Main Methods:
- Design of a state observer tailored for fractional-order systems.
- Application of stability results from fractional-order system theory.
- Utilization of the pole placement method for error system stabilization.
- Mathematical analysis to prove the stability of fractional-order error systems.
Main Results:
- Successful implementation of complex modified projective synchronization in nonlinear fractional-order complex chaotic systems.
- Proof of stability for the fractional-order error systems.
- Demonstration of the method's effectiveness and wide applicability, including fractional-order hyper-chaotic systems.
- Validation through two numerical examples.
Conclusions:
- The proposed state observer-based method effectively achieves complex modified projective synchronization.
- The synchronization strategy is robust and applicable to a wide range of fractional-order chaotic systems.
- The method's proven stability and engineering applicability make it a valuable contribution to the field.
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