General Decay Stability of Theta Approximations for Stochastic Delay Hopfield Neural Networks

This paper investigates the general decay stability of the stochastic linear theta (SLT) method and the split-step theta (SST) method for stochastic delay Hopfield neural networks. The definition of general decay stability for numerical solutions is formulated. Sufficient conditions are derived to ensure the general decay stability of the SLT and SST methods, respectively. The key findings reveal that, under the derived sufficient conditions, both the SLT and SST methods can achieve general decay stability when θ∈12,1, while for the case of θ∈0,12, the stability can also be guaranteed, which requires a stronger constraint on the step size. Finally, numerical examples are provided to demonstrate the effectiveness and validity of the theoretical results.