研究目的
Investigating the stability of numerical schemes for time varying delayed stochastic Hopfield neural networks.
研究成果
The Euler–Maruyama scheme is mean square exponentially stable for step sizes below a theoretical upper bound, while the backward Euler–Maruyama scheme is stable for all step sizes. The stability indices converge to those of the continuous model as step size approaches zero, and the methods are robust to variations in time delays.
研究不足
The stability criteria are specific to exponential stability and may not apply to asymptotically stable systems; the numerical schemes require solving implicit equations, which can be computationally intensive.
1：Experimental Design and Method Selection:
The paper designs Euler–Maruyama and backward Euler–Maruyama numerical schemes for the model, reformulates the contractive mapping principle for stability analysis, and uses It?'s rule and Lyapunov function methods.
2：Sample Selection and Data Sources:
The model involves stochastic differential equations with time-varying delays; initial data are given as continuous functions on specified intervals.
3：List of Experimental Equipment and Materials:
No specific equipment or materials are mentioned; the work is theoretical and computational.
4：Experimental Procedures and Operational Workflow:
Numerical schemes are implemented with step size adjustments; stability is analyzed through mean square exponential estimates and contractive mapping.
5：Data Analysis Methods:
Monte Carlo simulations with 1000 runs are used for numerical verification; stability criteria are derived using inequalities and transcendental equations.
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