含无畸变传输线电磁系统中的非线性现象分析

Analysis of the Nonlinear Phenomenon in an Electromagnetic System with Distortionless Transmission Line

建立了终端接二极管的含无畸变传输线无穷维电磁系统模型,利用特征法并结合系统边界条件得到了系统左端点处电压的Poincaré映射关系.应用非线性动力学理论分析了左端点处电压映射的定点稳定性及其动力学过程.结合数值仿真结果,详细分析了随参数变化系统发生的分岔与混沌现象,并对直流偏置电源对系统动力学行为的影响进行了研究.研究结果表明,在一定参数条件下,该电磁系统存在分岔、混沌、间歇性混沌等复杂的非线性动力学行为,直流偏置电源的存在加速了由倍周期分岔通向混沌的过程.

An infinite-dimensional electromagnetic system model with distortionless transmission line of the terminal diode was developed. Based on the boundary conditions, an Poincar6 map of the voltage wave at the left end of the system was derived by using the characteristics method. The stability at the fixed point and the dynamical behaviors of the map of the voltage wave at the left end were analyzed based on nonlinear dynamics theory. Thanks to numerical results, the phenomena of bifurcations and chaos of the system were analyzed with the variation of system parameter in detail, and the effects of the DC bias voltage source on the dynamics behaviors of the system were investigated. These research results show that there are complex nonlinear dynamical behaviors in this electromagnetic system under certain parametric condition, such as bifurcation, chaos and intermittent chaos and so on, and the presence of the DC bias voltage source accelerates the routes from period-doubling bifurcations to chaos.