Department of Engineering Mathematics, University of Bristol, Queen's Building, Bristol BS8 1TR, United Kingdom.
Phys Rev Lett. 2011 Jun 24;106(25):254103. doi: 10.1103/PhysRevLett.106.254103.
Discontinuous time derivatives are used to model threshold-dependent switching in such diverse applications as dry friction, electronic control, and biological growth. In a continuous flow, a discontinuous derivative can generate multiple outcomes from a single initial state. Here we show that well-defined solution sets exist for flows that become multivalued due to grazing a discontinuity. Loss of determinism is used to quantify dynamics in the limit of infinite sensitivity to initial conditions, then applied to the dynamics of a superconducting resonator and a negatively damped oscillator.
不连续时间导数用于对各种应用中的阈值相关切换进行建模，例如干摩擦、电子控制和生物生长。在连续流中，不连续导数可以从单个初始状态生成多个结果。在这里，我们表明，由于掠过不连续点而变得多值的流存在明确的解集。利用对初始条件的无限敏感性来定量动力学的耗散，然后将其应用于超导谐振器和负阻尼振荡器的动力学。
