带有周期性外加扰动的广义高阶非线性薛定谔方程的混沌及控制分析

he nonlinear dynamics of a generalized higher-ordernonlinear Schr"{o}dinger (HNLS) equation with a periodic externalperturbation is investigated numerically. Via the phase planeanalysis, it's found that both the homoclinic orbits andheteroclinic orbits can exist for the unperturbed HNLS equationunder certain conditions. Moreover, under the effect of the periodicexternal perturbation, the quasi-periodic bifurcations arise and canevolve into the chaos. The dynamical responses of the perturbed HNLSequation with regard to the perturbation strength are simulatedthrough the bifurcation diagrams, maximum Lyapunov exponents andphase portraits, which further prove the existence of the chaos forthe HNLS equation with a periodic external perturbation.Furthermore, two methods are used to control the chaos effectively,which can make the chaotic motions evolve into the stablequasi-periodic orbits. Those studies are helpful to reveal thedynamical properties of the HNLS equation.