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Quasi-synchronization for variable-order fractional complex dynamical networks with hybrid delay-dependent impulses
Chen Wei1, Xiaoping Wang1, Fangmin Ren1
1School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China.
Summary
This study investigates quasi-synchronization in complex dynamical networks with variable-order fractional derivatives and hybrid impulses. A novel criterion ensures network synchronization, validated by numerical examples.
Area of Science:
- Complex dynamical networks
- Fractional calculus
- Control theory
Background:
- Heterogeneous variable-order fractional complex dynamical networks (VFCDNs) present unique synchronization challenges.
- Hybrid delay-dependent impulses and mismatched parameters complicate network dynamics.
Purpose of the Study:
- To establish a more practical mathematical model for VFCDNs with short memory.
- To develop a novel criterion for achieving quasi-synchronization in VFCDNs with hybrid delay-dependent impulses.
Main Methods:
- Development of a novel fractional differential inequality under the variable-order fractional derivative framework.
- Application of differential inclusion theory and the Lyapunov method.
- Construction of a mathematics model for VFCDNs with multi-weighted networks and mismatched parameters.
Main Results:
- A new criterion for quasi-synchronization in VFCDNs with hybrid delay-dependent impulses is derived.
- The proposed model and criterion are demonstrated to be practical and feasible through numerical simulations.
Conclusions:
- The study successfully addresses quasi-synchronization in complex VFCDNs with hybrid impulses.
- The findings contribute to the theoretical understanding and practical control of such dynamical systems.
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