论文标题
通过重置在确定性系统中缓解长时间的短暂时间
Mitigating long transient time in deterministic systems by resetting
论文作者
论文摘要
在动态系统吸引力的盆地中达到稳定的平衡点需要多长时间?这是一个非常普遍的兴趣的问题,并且在动态和随机系统中刺激了许多活动,在这种动态和随机系统中,该估计的度量通常被称为瞬态或第一次传递时间。在非线性系统中,由于其潜在的动态,经常会经历较长的瞬变。我们应用重置或重新启动,这是统计物理和随机过程中的新兴概念,以减轻确定性动力学系统中延长瞬变的有害影响。我们表明,在间歇时间停止正在进行的过程只能从空间控制线重新启动,可以大大加快其完成,从而导致平均瞬态时间大大减少。此外,我们的研究逐渐减少了平均值的波动。我们的主张是在不同的重置策略下对Stuart-Landau极限周期振荡器和混乱的Lorenz系统进行详细的数值研究确立的。我们的分析通过将原始动力学与外部随机或周期性计时器统一,为瞬态时间的均值和波动打开了一扇门,并在利用动态系统中利用最佳方式的最佳方式提出了开放问题。
How long does a trajectory take to reach a stable equilibrium point in the basin of attraction of a dynamical system? This is a question of quite general interest, and has stimulated a lot of activities in dynamical and stochastic systems where the metric of this estimation is often known as the transient or first passage time. In nonlinear systems, one often experiences long transients due to their underlying dynamics. We apply resetting or restart, an emerging concept in statistical physics and stochastic process, to mitigate the detrimental effects of prolonged transients in deterministic dynamical systems. We show that stopping an ongoing process at intermittent time only to restart all over from a spatial control line, can dramatically expedite its completion, resulting in a huge decrease in mean transient time. Moreover, our study unfolds a net reduction in fluctuations around the mean. Our claim is established with detailed numerical studies on the Stuart-Landau limit cycle oscillator and chaotic Lorenz system under different resetting strategies. Our analysis opens up a door to control the mean and fluctuations in transient time by unifying the original dynamics with an external stochastic or periodic timer, and poses open questions on the optimal way to harness transients in dynamical systems.