Stability Switches in a First-Order Complex Neutral Delay Equation

by transforming the complex equation into two coupled real DDEs. In [5], Wei and Zhang considered the same equation and, by studying the distribution of the roots of the characteristic equation for the associated real differential system with delay, analyzed the existence of stability switches [6–8]. Transforming a complex DDE into two coupled real DDEs to analyze its stability has some drawbacks, as, in general, the orders of the characteristic quasipolynomials to be analyzed double, and, since the study of the distribution of their roots is much more complicated as their degrees increase, it becomes very difficult to obtain necessary and sufficient conditions of stability [1, 9, 10]. To avoid this problem, recently Li et al. [11] presented a method for directly analyzing the stability of complex DDEs on the basis of stability switches.Their results generalize those for real DDEs, thus greatly reducing the complexity of the analysis. In this paper, the results developed in [11] will be used to study the stability switches of the zero solution of the neutral equation (1).