Improved Results on Fixed-/Preassigned-Time Synchronization for Memristive Complex-Valued Neural Networks.

Area of Science:

• Control Theory
• Computational Neuroscience
• Nonlinear Dynamics

Background:

• Memristive complex-valued neural networks (MCVNNs) present unique synchronization challenges due to their complex-valued nature.
• Existing synchronization methods often lack precision in settling time or require complex system decomposition.

Purpose of the Study:

• To develop advanced control strategies for achieving fixed-time synchronization (FXTS) and pre-assigned-time synchronization (PATS) in MCVNNs.
• To establish more accurate fixed-time stability theorems and settling time estimations.
• To design simpler controllers that avoid decomposing complex-valued systems.

Main Methods:

• Application of the comparison principle for establishing fixed-time stability theorems.
• Development of novel discontinuous controllers utilizing different norms of complex numbers.
• Introduction of new control strategies for pre-assigned-time synchronization (PATS).

Main Results:

• Achieved more comprehensive fixed-time stability theorems and accurate settling time (ST) estimations.
• Designed simpler controllers leading to improved FXTS results without real/imaginary part decomposition.
• Demonstrated pre-assigned-time synchronization (PATS) where ST is independent of initial conditions and system parameters.

Conclusions:

• The proposed synchronization methodologies offer superior performance and control over MCVNNs.
• The new approaches provide faster and more predictable synchronization compared to existing methods.
• Numerical simulations validate the effectiveness and advantages of the developed synchronization techniques.