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Control and switching synchronization of fractional order chaotic systems using active control technique
A G Radwan1, K Moaddy2, K N Salama3
1Engineering Mathematics, Faculty of Engineering, Cairo University, Egypt.
Journal of Advanced Research
|February 17, 2015
Summary
This study explores how fractional order affects the Lü system
Area of Science:
- Nonlinear Dynamics
- Chaos Theory
- Fractional Calculus
Background:
- The Lü system is a well-known chaotic system.
- Fractional-order systems exhibit complex behaviors.
- Synchronization of chaotic systems is crucial for applications.
Purpose of the Study:
- To investigate the impact of fractional order on the Lü system's dynamics.
- To demonstrate synchronization between different fractional-order chaotic systems.
- To explore static and dynamic synchronization using active control.
Main Methods:
- Nonstandard finite difference method for numerical solutions.
- Active control technique for synchronization.
- Analysis of system response with varying fractional orders.
Main Results:
- Fractional order influences the Lü system's transition from stable to chaotic to periodic states.
- Successful synchronization of fractional-order chaotic systems achieved.
- Static and dynamic synchronization demonstrated with time-varying parameters.
Conclusions:
- Fractional order is a key parameter in controlling chaotic system dynamics.
- Active control is effective for synchronizing fractional-order chaotic systems.
- The nonstandard finite difference method provides accurate numerical solutions.
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