Energy loss and noise by chaotic motion of magnetic spin

通过积分阻尼项计算了畴壁运动引起的能量损失。结合分岔图讨论了能量损失的值。能量损失在第一次过渡到混沌时跳到一个很高的值。结果表明，在相同的阻尼系数下，周期窗口内的能量损失大于相邻混沌区域的能量损失;计算了畴壁运动的混沌区域随外加磁场的幅值和频率的变化.它显示出由规则和混乱区域组成的复杂图案。计算了畴壁运动的能量损失和李雅普诺夫指数。能量损失对频率曲线的峰值处的频率，即非线性谐振频率，与线性理论中的谐振频率不同，因为其随着外部磁驱动场的振幅的增加而向较低频率偏移。这种峰移可以用以下效应来解释： ...更多信息 非线性恢复力中的高阶项。在李雅普诺夫指数为正的混沌区，能量损失随频率的变化曲线变得不规则，能量损失减小.针对两步OGY方法和预测OGY方法控制磁畴壁运动混沌的问题，提出了两步OGY方法和预测OGY方法.在两步OGY方法中，磁畴壁首先在周期轨道上移动，当轨道接近鞍点时使用OGY方法。在预测OGY方法中，在应用OGY方法之前预测磁畴壁的运动。利用畴壁运动的时间序列，可以重构出状态空间中的吸引子。即使在混沌系统中，近期的未来也可以被预测，因为被预测者在吸引子中的邻域系统的短期发展彼此没有太大的不同。改进后的OGY法的建立时间是原OGY法的1/5-1/30。少

The energy loss caused by the domain-wall motion is calculated by integrating damping term. The value of the energy loss is discussed in connection with the bifurcation diagram. The energy loss jumps to a high value at the first transition to chaos. The energy loss in the periodic window is larger than the value in the neighboring chaotic region in spite of their having the same damping coefficient.A chaotic region of domain wall motion is calculated as a function of the amplitude and frequency of the external magnetic drive field. It shows an intricate pattern composed of regular and chaotic regions. An energy loss and the Lyapunov exponent of domain wall motion are calculated. A frequency at the peak of the energy loss versus frequency curve, namely a nonlinear resonance frequency, is different from a resonance frequency in the linear theory as it shifts toward a lower frequency with increasing amplitude of the external magnetic drive field. This peak shift is explained by the effect … More of the higher order term in the nonlinear restoring force. The energy loss versus frequency curve becomes irregular and the energy loss decreases in the chaotic region where the Lyapunov exponent is positive.The two-step Ott-Grebogi-Yorke (OGY) method and the prediction OGY method for controlling chaos of magnetic domain-wall motion are proposed to improve the long settling time in the original OGY method. In the two-step OGY method, a magnetic domain wall is first moved on a periodic orbit and the OGY method is used when the orbit approaches a saddle point. In the prediction OGY method, the motion of the domain wall is predicted before the OGY method is applied. An attractor in the state space can be reconstructed by using the time series of the domain-wall motion. The near future can be predicted even in the chaotic system, because the short time developments of the neighborhood system of a predictee in the attractor are not so different from each other. The settling time of the improved OGY methods is 1/5-1/30 times as long as that of the original OGY method. Less