Dynamic Behavior and Fixed-Time Synchronization Control of Incommensurate Fractional-Order Chaotic System
Abstract
1. Introduction
2. Preliminaries, Modeling, and Algorithms
2.1. Preliminaries
2.2. Modeling and Algorithms
3. Dynamic Analysis
3.1. Incommensurate Aystem Phase Diagram and Poincaré Analysis
3.2. Dynamic Analysis of Fractional Orders Change in Incommensurate System
3.3. Coexistence Dynamics Phenomenon of Incommensurate System Parameter Changes
3.3.1. Dynamic Phenomena of Parameter a Change
3.3.2. Dynamic Phenomena of Parameter b Change
3.3.3. Dynamic Phenomena of Parameter d Change
3.3.4. Dynamic Phenomena of Parameter f Change
3.4. Dynamic Behavior of Chaotic Degeneration in Incommensurate Fractional-Order System
4. Analog Circuit Implementation of Incommensurate System
5. Fixed-Time Synchronization Control of Incommensurate System
5.1. Main Discussion
5.2. Simulation Results
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Wang, X.; Wang, Z.; Dang, S. Dynamic Behavior and Fixed-Time Synchronization Control of Incommensurate Fractional-Order Chaotic System. Fractal Fract. 2025, 9, 18. https://doi.org/10.3390/fractalfract9010018
Wang X, Wang Z, Dang S. Dynamic Behavior and Fixed-Time Synchronization Control of Incommensurate Fractional-Order Chaotic System. Fractal and Fractional. 2025; 9(1):18. https://doi.org/10.3390/fractalfract9010018
Chicago/Turabian StyleWang, Xianchen, Zhen Wang, and Shihong Dang. 2025. "Dynamic Behavior and Fixed-Time Synchronization Control of Incommensurate Fractional-Order Chaotic System" Fractal and Fractional 9, no. 1: 18. https://doi.org/10.3390/fractalfract9010018
APA StyleWang, X., Wang, Z., & Dang, S. (2025). Dynamic Behavior and Fixed-Time Synchronization Control of Incommensurate Fractional-Order Chaotic System. Fractal and Fractional, 9(1), 18. https://doi.org/10.3390/fractalfract9010018