Fractional-order stochastic delayed neural networks with impulses: mean square finite-time contractive...

Area of Science:

• Control Theory
• Neural Networks
• Stochastic Systems

Background:

• Fractional-order systems exhibit memory and hereditary properties.
• Stochastic delayed neural networks present complex dynamics.
• Finite-time synchronization is crucial for real-time applications.

Purpose of the Study:

• To develop a novel hybrid control framework for mean square finite-time synchronization (MSFTSn) and mean square finite-time contractive synchronization (MSFTCSn).
• To address synchronization challenges in fractional-order stochastic delayed neural networks (FOSDNNs).

Main Methods:

• Integration of stochastic analysis, Lyapunov-based methods, fractional Gronwall inequality, and an improved Razumikhin framework.
• Application of set-valued map theory for discontinuous neuron activation functions.
• Hybrid control combining continuous feedback and impulsive regulation.

Main Results:

• Novel synchronization criteria for FOSDNNs were established.
• The hybrid control strategy guarantees finite-time synchronization of the error system.
• Demonstrated extension of stabilizing parameter ranges compared to standard feedback schemes.
• Validated effectiveness and robustness through numerical simulations.

Conclusions:

• The proposed hybrid control is effective for MSFTSn and MSFTCSn in FOSDNNs.
• Fractional derivatives enhance neural network representation by incorporating memory effects.
• The framework offers improved convergence rates and enhanced contractive stability.