弱受迫极限环振子全局卷吸的周期输入波形优化
Optimization of periodic input waveforms for global entrainment of weakly forced limit-cycle oscillators
摘要：
本文提出了一种基于相位缩减和非线性规划的弱受迫极限环振子全局卷吸的周期输入波形优化方法。我们从弱周期输入驱动的极限环振荡器的数学模型中推导出平均相位动力学，并优化输入波形的傅立叶系数以最大化规定的目标函数。与依赖于变分法的优化方法相比，所提出的方法可以应用于更广泛的优化问题，包括全局夹带目标。作为一个例子，我们考虑两个优化问题，一个是实现快速的全局收敛的振荡器的夹带状态和其他实现规定的全球相位分布在人口相同的非耦合噪声振荡器。我们表明，所提出的方法可以成功地产生最佳的输入波形，以实现在这两种情况下所需的状态。
英文摘要：
We propose a general method for optimizing periodic input waveforms for global entrainment of weakly forced limit-cycle oscillators based on phase reduction and nonlinear programming. We derive averaged phase dynamics from the mathematical model of a limit-cycle oscillator driven by a weak periodic input and optimize the Fourier coefficients of the input waveform to maximize prescribed objective functions. In contrast to the optimization methods that rely on the calculus of variations, the proposed method can be applied to a wider class of optimization problems including global entrainment objectives. As an illustration, we consider two optimization problems, one for achieving fast global convergence of the oscillator to the entrained state and the other for realizing prescribed global phase distributions in a population of identical uncoupled noisy oscillators. We show that the proposed method can successfully yield optimal input waveforms to realize the desired states in both cases.
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