As a human brain-like computational model that can reflect the cognitive function of the brain, the problem of dynamic analysis of associative memory neural networks has attracted the attention of scholars. This paper combines associative memory neural networks with enterprise financial management risks, studies the synchronization control and stability analysis problems of unidirectional associative memory-like human brain amnestic neural networks with perturbation and mixed time-varying time lags, proposes a bidirectional associative memory-like brain stochastic amnestic neural network model with mixed time-varying time lags, designs a discrete-time sampling control strategy based on the model, and studies various types of recent financial risks. Based on the early warning research, based on the associative memory neural network method, we propose to reconstruct the risk categories, including improving the enterprise risk management system, enhancing the awareness of financial risk management from top to bottom, and strengthening the core competitiveness of the enterprise itself and control measures for financing, investment, operation, and cash flow risks.