This article investigates the dynamic properties of two-dimensional nonlinear magnetic metamaterials consisting of nanoscale elements. The authors propose a model for a two-dimensional lattice of capacitively and inductively coupled split rectangular nanoresonators. It has been shown that the long-wave dynamics of this two-dimensional lattice are described by a regularized two-dimensional nonlinear Klein–Gordon equation, which has been solved in the form of two sequences of two-dimensional dynamic solitons on a pedestal of homogeneous forced oscillations, using an asymptotic method and taking into account the action of electromotive force (EMF) induced by an electromagnetic wave. The authors have calculated a diamagnetic response to an electromagnetic field in the terahertz range in the metamaterial region, where a breather is excited and oscillates in antiphase to a homogeneous background. The evolution of long-lived metastable breathers has been numerically studied, and two scenarios – collapse and decay – have been established for the development of their instability depending on the parameters of the induced EMF and inductive coupling between nanoresonators. It has been found that at the boundary between these scenarios, the final result of the transformation of the breathers is the chimera state of the metamaterial with a large-amplitude breather that generates stochastic waves.

中文翻译：

---

二维非线性超材料中的亚稳态呼吸器和局部抗磁性

本文研究了由纳米级元素组成的二维非线性磁性超材料的动态特性。作者提出了电容和电感耦合分裂矩形纳米谐振器的二维晶格模型。已经表明，这种二维晶格的长波动力学是由正则化的二维非线性 Klein-Gordon 方程描述的，该方程已以二维动态孤子的两个序列的形式在均匀受迫振荡，使用渐近方法并考虑到由电磁波引起的电动势 (EMF) 的作用。作者计算了对超材料区域中太赫兹范围内的电磁场的抗磁响应，其中呼吸器被激发并与均匀背景反相振荡。已经对长寿命亚稳态呼吸器的演变进行了数值研究，并且根据感应电动势和纳米谐振器之间的感应耦合的参数，已经建立了两种情况——坍塌和衰变——来发展它们的不稳定性。已经发现，在这些场景之间的边界处，呼吸器转换的最终结果是超材料的嵌合状态，具有产生随机波的大振幅呼吸器。根据感应电动势的参数和纳米谐振器之间的感应耦合，已经建立了两种情景——坍塌和衰变，以发展它们的不稳定性。已经发现，在这些场景之间的边界处，呼吸器转换的最终结果是超材料的嵌合状态，具有产生随机波的大振幅呼吸器。根据感应电动势的参数和纳米谐振器之间的感应耦合，已经建立了两种情景——坍塌和衰变，以发展它们的不稳定性。已经发现，在这些场景之间的边界处，呼吸器转换的最终结果是超材料的嵌合状态，具有产生随机波的大振幅呼吸器。