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Fixed-deviation stabilization and synchronization for delayed fractional-order complex-valued neural networks.

Bingrui Zhang¹, Jin-E Zhang¹

¹School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China.

Mathematical Biosciences and Engineering : MBE

|June 16, 2023

Summary

This summary is machine-generated.

This study explores fixed-deviation stabilization and synchronization for delayed fractional-order complex-valued neural networks. New conditions ensure stability and synchronization using a linear discontinuous controller.

Keywords:

discontinuous control fixed-deviation dynamics fractional-order complex-valued neural networks time delays

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Area of Science:

Complex-valued neural networks
Fractional-order systems
Control theory

Background:

Fractional-order systems offer enhanced modeling capabilities over integer-order systems.
Complex-valued neural networks are crucial for processing complex data.
Synchronization and stabilization are key challenges in neural network research.

Purpose of the Study:

To investigate fixed-deviation stabilization and synchronization for fractional-order complex-valued neural networks with delays.
To develop a linear discontinuous controller for achieving these objectives.
To validate the proposed theoretical framework through simulations.

Main Methods:

Application of fractional calculus principles.
Utilizing fixed-deviation stability theory.
Design and implementation of a linear discontinuous controller.

Main Results:

Sufficient conditions derived for fixed-deviation stabilization.
Sufficient conditions derived for fixed-deviation synchronization.
Demonstration of controller effectiveness via two simulation examples.

Conclusions:

The proposed method effectively achieves fixed-deviation stabilization and synchronization.
The theoretical results are validated by simulation examples.
The study contributes to the control of complex fractional-order neural networks.