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.

中文翻译：

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晶格动力系统多脉冲解的孤立体

这项工作研究了双稳态晶格动力学系统的多脉冲稳态解的存在和分岔结构。这种解决方案的特点是多个紧致断开区域，其中解决方案类似于其中一个双稳态，并且类似于这些紧集之外的另一个平凡双稳态。结果表明，即使单脉冲解位于无界曲线上，这些多脉冲解的分岔曲线也位于闭合和有界曲线（isolas）上。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反连续极限附近通过分析得到证实。结果通过一些数值研究得到证明。