论文标题
三维非线性反对称Lotka-Volterra系统中受拓扑保护的动力学
Topologically protected dynamics in three-dimensional nonlinear antisymmetric Lotka-Volterra systems
论文作者
论文摘要
拓扑带及其相关的低维边界模式的研究主要集中在线性系统上。这项工作报告了三维（3D）非线性系统的强大动力学特征，与3D中有趣的拓扑结构有关。具体而言，对于固有非线性的反对称lotka-volterra方程（ALVE）支配的耦合岩纸剪膜循环的3D设置，我们在表面极化群众的固有特征和鲁棒性中，并在与线性化lotka-volterra的动力学频段（lv volvolterra（lv）相关的情况下，我们揭示了它们的独特特征和鲁棒性。我们的分析表明，从牙槽的线性化版本的I型和II类型Weyl奇异性的Weyl半学相中学到的见解仍然非常有用，即使系统动力学远远超出了线性状态。这项工作表明了拓扑边界模式在分析高维非线性系统中的相关性和重要性，并希望刺激非线性系统中的另一波拓扑研究。
Studies of topological bands and their associated low-dimensional boundary modes have largely focused on linear systems. This work reports robust dynamical features of three-dimensional (3D) nonlinear systems in connection with intriguing topological bands in 3D. Specifically, for a 3D setting of coupled rock-paper-scissors cycles governed by the antisymmetric Lotka-Volterra equation (ALVE) that is inherently nonlinear, we unveil distinct characteristics and robustness of surface polarized masses and analyze them in connection with the dynamics and topological bands of the linearized Lotka-Volterra (LV) equation. Our analysis indicated that insights learned from Weyl semimetal phases with type-I and type-II Weyl singularities based on a linearized version of the ALVE are still remarkably useful, even though the system dynamics is far beyond the linear regime. This work indicates the relevance and importance of the concept of topological boundary modes in analyzing high-dimensional nonlinear systems and hopes to stimulate another wave of topological studies in nonlinear systems.
