A novel predefined-time projective synchronization strategy for multi-modal memristive neural networks.

Area of Science:

• Control Theory
• Neural Networks
• Nonlinear Dynamics

Background:

• Predefined-time synchronization is crucial for complex systems but challenging in multimodal memristive neural networks.
• Existing methods lack generality and leniency in stability conditions.

Purpose of the Study:

• To systematically address the research gap in predefined-time synchronization for multimodal memristive neural networks.
• To develop a novel, more general stability theorem and a practical controller for achieving this synchronization.

Main Methods:

• Proposed a novel predefined-time stability theorem with relaxed conditions.
• Utilized theories of differential inclusion, Filippov solutions, and set-valued mapping.
• Designed a simple feedback controller based on the new stability theorem.

Main Results:

• The proposed stability theorem offers more lenient judgment conditions, enhancing applicability.
• A practical feedback controller was developed for predefined-time projective synchronization.
• Simulation experiments validated the theoretical framework's effectiveness and feasibility.

Conclusions:

• This research pioneers the systematic study of predefined-time synchronization in these networks.
• The developed methods and controller offer a more general and practical approach to system synchronization.