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The Intricacies of Sprott-B System with Fractional-Order Derivatives: Dynamical Analysis, Synchronization, and
Rending Lu1, Prasina Alexander2, Hayder Natiq3
1School of Electronic Engineering, Changzhou College of Information Technology, Changzhou 213164, China.
Entropy (Basel, Switzerland)
|September 28, 2023
Summary
Investigating fractional-order derivatives in the Sprott-B chaotic system enhances modeling and control. This study reveals complex dynamics and synchronization behaviors, validated by electronic circuit implementations for potential secure communications.
Area of Science:
- Nonlinear Dynamics and Chaos Theory
- Fractional Calculus Applications
- Complex Systems Modeling
Background:
- Fractional-order derivatives offer improved modeling accuracy and control capabilities for chaotic systems.
- The Sprott-B system is a fundamental simple chaotic system whose dynamics can be further explored.
- Understanding fractional-order dynamics is crucial for advancing chaos-based technologies.
Purpose of the Study:
- To investigate the dynamics of the Sprott-B chaotic system using fractional-order derivatives.
- To analyze the impact of fractional orders on system complexity, attractors, and synchronization.
- To experimentally validate theoretical findings through electronic circuit implementation.
Main Methods:
- Comprehensive dynamical analysis using bifurcation diagrams.
- Examination of system synchronization for various fractional derivative orders.
- Implementation of both integer-order and fractional-order electronic circuits for validation.
Main Results:
- Bifurcation analysis revealed the presence of coexisting attractors in the fractional-order Sprott-B system.
- Synchronization behavior was observed and analyzed across different fractional derivative orders.
- Experimental validation confirmed the theoretical predictions of the fractional-order system dynamics.
Conclusions:
- Fractional-order derivatives significantly enrich the dynamics of the Sprott-B system, offering enhanced complexity and control.
- The study provides a deeper understanding of fractional-order chaotic systems and their synchronization properties.
- Findings have potential implications for chaos-based secure communications and advanced nonlinear control systems.
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