Analyzing the Stability of Neural Networks with Delay Differential Equations

Neural networks are powerful computational models widely used in various domains, including machine learning, neuroscience, and control systems. However, the stability analysis of neural networks with time delays remains a challenging problem due to the complex interactions between neurons and the presence of delayed feedback loops. In this paper, we propose a novel approach to analyze the stability of neural networks using delay differential equations (DDEs). We begin by formulating a mathematical model of the neural network dynamics, incorporating time delays to account for the finite propagation time of signals between neurons. We then derive a set of delay differential equations that describe the evolution of the network states over time, taking into consideration the delayed interactions between neurons.