Investigating Uniform Stability of Fractional-Order Complex-Valued Stochastic Neural Networks with Impulses via a Direct Method

This paper focuses on exploring the existence and uniqueness of solutions for a specific type of impulsive fractional-order complex-valued stochastic neural network within the complex domain, a topic hitherto undocumented. The combination of fractional order, stochastic nature, complex values, and impulses allows the model to seize memory-related, noise-resilient, phase-sensitive, and discontinuous dynamics. These dynamics are crucial for applications in neuroscience, signal processing, engineering control, and time-series prediction. In contrast to more simplistic models, this framework provides greater fidelity when simulating real-world systems and wider applicability without the need for redundant component splitting, thus justifying the requirement for such a comprehensive model. Leveraging the contraction mapping principle and contradiction, sufficient conditions are deduced to guarantee the existence and uniform stability (in the distribution sense) of solutions for the impulsive fractional-order complex-valued stochastic neural networks under study. Finally, a numerical example is presented to illustrate the feasibility and precision of our findings.