Periodic External Input Tunes the Stability of Delayed Nonlinear Systems: From the Slaving Principle to Center Manifolds

摘要

The work illustrates a recent analysis technique that demonstrates that external periodic input affects the stability of the time-averaged nonlinear dynamics of a delayed system. At first, the article introduces the fundamental elements of delayed differential equations and then applies these to a nonlinear delayed problem close to a trans-critical bifurcation. We observe a shift of stability in the system induced by the fast periodic driving.