Period-1 Oscillations Of Two Kinds Of State-dependent Delayed Systems Via High-dimensional Harmonic Blance Method

State-dependent time-delayed systems are more realistic delayed systems in na-ture and human society. Their dynamic problems are a hot spot. The study on the existence and stability of the periodic solutions is an important topic. Under the support of the National Natural Science Foundation of China (No: 11372282),in this dissertation , Period one oscillations of the state-dependent delayed TCP mod-els with proportional integral enhanced (PIE) queue management policy and the van der Pol equation with exponential state-dependent delay are considered by the high-dimensional harmonic balance method (HDHBM) . Compared with the tradi-tional harmonic balance method, the HDHB method avoids the complex integration of the Fourier coefficients of the nonlinear right hand of the systems by solving the time domain variables of the Fourier coefficients at equally spaced sub-time over the period of one cycle of motion. Thus it transforms the problem into a relatively simple nonlinear algebraic equations, which greatly reduces the computation. By the HDHB method, the approximate expression of the periodic solutions for the two state-dependent delayed systems are obtained. We compare their amplitudes and phase portraits with those of the DDE-BIFTOOL. They agree well with each oth-er. It verifies the correctness and validity of the employed method.It turns out that many parameters of the state-dependent delayed TCP models with PIE queue man-agement policy play a very important role in their dynamic behaviours. As a result,we should control the parameters in a proper range to achieve our desired network performances.