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Multistability and fixed-time multisynchronization of switched neural networks with state-dependent switching rules
Shiqin Ou1, Zhenyuan Guo2, Shiping Wen3
1School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China.
Summary
This study explores multistability and fixed-time synchronization in switched neural networks, revealing 3^n stable solutions and synchronization manifolds. It introduces fixed-time multisynchronization for complex neural network dynamics.
Area of Science:
- Theoretical neuroscience
- Complex systems dynamics
- Nonlinear control theory
Background:
- Switched neural networks exhibit complex behaviors due to state-dependent switching and multiple solutions.
- Understanding multistability and synchronization is crucial for designing advanced neural network models.
Purpose of the Study:
- To theoretically analyze multistability and fixed-time synchronization in switched neural networks.
- To introduce and investigate fixed-time multisynchronization for the first time.
- To characterize the number, location, and stability of almost-periodic solutions.
Main Methods:
- State-space partition for characterizing solution properties.
- Derivation of sufficient conditions for the existence of 3^n stable solutions.
- Analysis of multistability to establish synchronization manifolds.
Main Results:
- Characterization of the number, location, and stability of almost-periodic solutions.
- Existence of 3^n exponentially stable almost-periodic solutions.
- Introduction of fixed-time multisynchronization with 3^n synchronization manifolds.
- Estimation of settling time for drive-response synchronization.
Conclusions:
- The study provides a theoretical framework for understanding multistability and fixed-time synchronization in switched neural networks.
- Novel insights into the complex dynamics and synchronization capabilities of these networks are presented.
- The findings have implications for the design and control of complex neural systems.
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