Nonseparation Method-Based Finite/Fixed-Time Synchronization of Fully Complex-Valued Discontinuous Neural Networks

Area of Science:

• Complex dynamical systems
• Neural network theory
• Control theory

Background:

• Synchronization is crucial for complex-valued delayed neural networks.
• Existing methods often require separating networks into real and imaginary parts, which is complex.
• Discontinuous activations and time-varying delays pose significant challenges.

Purpose of the Study:

• To develop novel methods for finite and fixed-time synchronization of complex-valued delayed neural networks.
• To avoid the separation of complex networks into real subsystems.
• To propose discontinuous control strategies and analyze synchronization criteria.

Main Methods:

• A novel complex-valued sign function was proposed and its properties established.
• Two discontinuous control strategies were developed using quadratic and a new absolute-value-based norm.
• Nonsmooth analysis and novel inequality techniques in the complex field were applied.

Main Results:

• Synchronization criteria and settling time estimates were derived for complex-valued delayed neural networks.
• A unified control strategy was designed under the new norm framework.
• A single controller parameter was found to determine finite or fixed-time synchronization.

Conclusions:

• The proposed methods effectively achieve finite and fixed-time synchronization without network separation.
• The novel norm and control strategy offer a unified approach to synchronization.
• The findings contribute to the theoretical understanding and practical control of complex dynamical systems.