论文标题
晶格动力学系统的多脉冲解决方案的隔离
Isolas of multi-pulse solutions to lattice dynamical systems
论文作者
论文摘要
这项工作调查了多脉冲稳态解决方案对双晶格动力学系统的存在和分叉结构。这样的解决方案的特征是多个紧凑的断开区域，在这些区域中，该解决方案类似于Bistable状态之一，并且类似于这些紧凑型集合之外的另一个微不足道的双向状态。结果表明，即使单脉冲溶液沿无限的曲线，这些多脉冲溶液的分叉曲线也位于封闭和有界的曲线（Iselas）。这些结果应用于离散的nagumo微分方程，我们表明，这项工作的假设可以在抗抗胞菌限制附近进行分析确认。通过许多数值研究证明了结果。
This work investigates the existence and bifurcation structure of multi-pulse steady-state solutions to bistable lattice dynamical systems. Such solutions are characterized by multiple compact disconnected regions where the solution resembles one of the bistable states and resembles another trivial bistable state outside of these compact sets. It is shown that the bifurcation curves of these multi-pulse solutions lie along closed and bounded curves (isolas), even when single-pulse solutions lie along unbounded curves. These results are applied to a discrete Nagumo differential equation and we show that the hypotheses of this work can be confirmed analytically near the anti-continuum limit. Results are demonstrated with a number of numerical investigations.
