A Geometric Method for Studying the Stability Switching Criteria with Two Discrete Delays

This paper studies the characteristic equations for a class of functional differential equations with two discrete delays, and a complete distribution of the characteristic roots is derived by a geometric method. With the method, one more type of stable switching curves is obtained. At first, the necessary and sufficient conditions for the existence of pure imaginary roots and crossing sets are established through the parallelogram rule. Then, after a careful analysis of the crossing set, the types of stable switching curves and the crossing direction are revealed. In addition, to validate the theoretical results obtained, an example of a neural network model with two discrete delays is presented.