论文标题
激发和较弱耗散的振荡系统中的自动兑现
Autoresonance in oscillating systems with combined excitation and weak dissipation
论文作者
论文摘要
考虑了一个数学模型，描述了具有组合参数和外部激发的非线性振荡系统的捕获的初始阶段。具有无限幅度和有限相位不匹配的溶液对应于自动捕获量。本文研究了系统中存在弱耗散的情况下这种解决方案的存在，稳定性和分叉。我们的技术基于对无限幂的特定解决方案的研究以及合适的Lyapunov功能的构建。
A mathematical model describing the initial stage of the capture into autoresonance for nonlinear oscillating systems with combined parametric and external excitation is considered. The solutions with unboundedly growing amplitude and limited phase mismatch correspond to the autoresonant capture. The paper investigates the existence, stability and bifurcations of such solutions in the presence of a weak dissipation in the system. Our technique is based on the study of particular solutions with power-law asymptotics at infinity and the construction of suitable Lyapunov functions.
