论文标题
非自治非线性动力学系统中的最佳时间平均
Optimal time averages in non-autonomous nonlinear dynamical systems
论文作者
论文摘要
辅助函数方法允许通过凸优化计算自主非线性普通微分方程中动态变量函数的极端长期平均值。对于由自主多项式矢量字段定义的动力系统，它在操作上是使用正方形技术总和的半决赛程序。在此贡献中，我们审查了该方法并将其扩展到适用于涉及动力学变量三角函数的定期驱动的非自治的非线性矢量场。介绍了阻尼驱动的驱动振荡器和定期驱动的摆动，以说明辅助函数方法的实用性。
The auxiliary function method allows computation of extremal long-time averages of functions of dynamical variables in autonomous nonlinear ordinary differential equations via convex optimization. For dynamical systems defined by autonomous polynomial vector fields, it is operationally realized as a semidefinite program utilizing sum of squares technology. In this contribution we review the method and extend it for application to periodically driven non-autonomous nonlinear vector fields involving trigonometric functions of the dynamical variables. The damped driven Duffing oscillator and periodically driven pendulum are presented as examples to illustrate the auxiliary function method's utility.
