Novičenko Viktor, Ratas Irmantas
Institute of Theoretical Physics and Astronomy, Vilnius University, Saulėtekio Avenue 3, LT-10222 Vilnius, Lithuania.
Center for Physical Sciences and Technology, Saulėtekio Avenue 3, LT-10222 Vilnius, Lithuania.
Phys Rev E. 2016 Dec;94(6-1):062213. doi: 10.1103/PhysRevE.94.062213. Epub 2016 Dec 20.
We analyze limit cycle oscillators under perturbation constructed as a product of two signals, namely, an envelope with a period close to natural period of an oscillator and a high-frequency carrier signal. A theory for obtaining an envelope waveform that achieves the maximal frequency interval of entrained oscillators is presented. The optimization problem for fixed power and maximal allowed amplitude is solved by employing the phase reduction method and the Pontryagin's maximum principle. We have shown that the optimal envelope waveform is a bang-bang-type solution. Also, we have found "inversion" symmetry that relates two signals with different powers but the same interval of entrained frequencies. The theoretical results are confirmed numerically on FitzHugh-Nagumo oscillators.
我们分析了在微扰下构建的极限环振荡器，该振荡器由两个信号的乘积构成，即一个周期接近振荡器自然周期的包络信号和一个高频载波信号。提出了一种用于获得能实现最大频率间隔的夹带振荡器的包络波形的理论。通过采用相位约化方法和庞特里亚金极大值原理，解决了固定功率和最大允许幅度的优化问题。我们已经表明，最优包络波形是一种Bang-Bang型解。此外，我们还发现了“反转”对称性，该对称性将具有不同功率但相同夹带频率间隔的两个信号联系起来。在菲茨休 - 纳古莫振荡器上对理论结果进行了数值验证。
