Impulsive control for stationary oscillation of nonlinear delay systems and applications

In this paper, the problem of existence-uniqueness and global exponential stability of periodic solution (i.e., stationary oscillation) for a class of nonlinear delay systems with impulses was studied. Some new sufficient conditions ensuring the existence of stationary oscillation for the addressed equations were derived by using the inequality technique that has been reported in recent publications. Our proposed method, which is different with the existing results in the literature, shows that nonlinear delay systems may admit a stationary oscillation using proper impulsive control strategies even if it was originally unstable or divergent. As an application, we considered the single species logarithmic population model and established a new criterion to guarantee the existence of positive stationary oscillation. Some numerical examples and their computer simulations were also given at the end of this paper to show the effectiveness of our development control method.