Instability of Solutions of Vector Lienard Equation With Constant Delay

Abstract

We consider the vector Lienard equation with the constant delay tau > 0, X ''(t) + F (X (t), X' (t))X' (t) + H (X (t - tau)) = 0. We establish certain sufficient conditions, which guarantee the instability of the zero solution of this equation. An example is given to illustrate the theoretical analysis in this work.