论文标题
时间耗散孤子的脉搏添加：谐音的同骨点和bis b的轨道翻转延迟
Pulse-adding of Temporal Dissipative Solitons: Resonant Homoclinic Points and the Orbit Flip of Case B with Delay
论文作者
论文摘要
我们从数值上研究了从一个脉冲的周期性行进波中的时间定位的，两脉冲的周期性行进波，其中具有延迟延迟的延迟微分方程（DDES），并具有较大延迟的延迟微分方程（DDES）。这种类型的解决方案通常称为应用程序中的时间耗散孤子（TDSS），我们在此处采用此术语。我们通过一个原型例子表明，与反应扩散部分微分方程（PDES）类似的脉冲类似 - 从一个脉冲TDS的两脉冲TDS分支由无激发尾巴组织由Codimension-Two two two two two two two suclibib equilibib equilibibib equiliLibib e a Traight a Travel Waver Waver frame frame frame frame frame frame frame frame trageimension tds。我们考虑了Sandstede模型的概括（用于研究Codimension-Two odes中的典型模型，其中包括ODES中的两个同层分叉点），并具有额外的减时参数，并使用自动07p和DDE-Biftool使用Auto07p和DDE-Biftool来数字地计算结果DDE中这些分离点的展开。然后，我们将此模型解释为DDE中TDSs的行驶波方程，并通过利用DDES周期溶液的重新出现，并以较大的延迟。在此过程中，我们将不可定向的共振同质分叉和案例$ \ mathbf {b} $的轨道翻转分叉是有组织的中心，以大量延迟在DDE中存在两个脉冲。此外，我们讨论了辅助系统中的同型分叉的折叠如何以大延迟限制DDE中TDS的存在区域。
We numerically investigate the branching of temporally localized, two-pulse periodic traveling waves from one-pulse periodic traveling waves with non-oscillating tails in delay differential equations (DDEs) with large delay. Solutions of this type are commonly referred to as temporal dissipative solitons (TDSs) in applications, and we adopt this term here. We show by means of a prototypical example that -- analogous to traveling pulses in reaction-diffusion partial differential equations (PDEs) -- the branching of two-pulse TDSs from one-pulse TDSs with non-oscillating tails is organized by codimension-two homoclinic bifurcation points of a real saddle equilibrium in a corresponding traveling wave frame. We consider a generalization of Sandstede's model (a prototypical model for studying codimension-two homoclinic bifurcation points in ODEs) with an additional time-shift parameter, and use Auto07p and DDE-BIFTOOL to compute numerically the unfolding of these bifurcation points in the resulting DDE. We then interpret this model as the traveling wave equation for TDSs in a DDE with large delay by exploiting the reappearance of periodic solutions in DDEs. In doing so, we identify both the non-orientable resonant homoclinic bifurcation and the orbit flip bifurcation of case $\mathbf{B}$ as organizing centers for the existence of two-pulse TDSs in the DDE with large delay. Additionally, we discuss how folds of homoclinic bifurcations in an auxiliary system bound the existence region of TDSs in the DDE with large delay.
