发表机构
Department of Mathematics, School of Science and Technology, Meiji University（明治大学理工学部数学系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究分布式延迟微分方程中记忆效应诱导的有限时间爆破，通过线性链技巧约化为二维ODE并分析无穷远动力学，发现记忆可加速爆破速率或转变爆破类型，且存在阈值现象控制爆破发生。
AI 中文摘要
本文研究了具有特定伽马分布核的、包含记忆效应的分布式延迟微分方程的有限时间爆破解。我们聚焦于在常微分方程（ODEs）中引起有限时间奇点的典型非线性项，考察记忆效应如何改变爆破的存在性、速率及定性性质。通过将这些行为与相应的无延迟且无记忆的常微分方程进行比较，我们表明源于记忆的时间延迟不仅本质上诱导有限时间爆破（“记忆诱导的爆破”），而且显著改变爆破轮廓，例如加速代数爆破速率或驱动从常微分方程淬灭到对数爆破的定性转变。此外，通过引入自抑制项，我们揭示了相空间中的一个阈值现象，该现象根据初始条件和参数控制爆破的发生与不发生。这些结果通过线性链技巧将系统约化为二维常微分方程，并利用庞加莱型紧化、爆破技术和中心流形定理分析无穷远处的动力学而建立。
英文摘要
In this paper, we investigate finite-time blow-up solutions for distributed delay differential equations incorporating memory effects with a specific gamma distribution kernel. Focusing on typical nonlinear terms that cause finite-time singularities in ordinary differential equations (ODEs), we examine how memory effects change the existence, rate, and qualitative properties of blow-up. By comparing these behaviors with those of the corresponding non-delayed and memory-free ODEs, we show that time delay originating from memory not only essentially induces finite-time blow-up (``memory-induced blow-up''), but also drastically alters the blow-up profile, such as accelerating algebraic blow-up rates or driving a qualitative transition from ODE quenching to logarithmic blow-up. Furthermore, by incorporating a self-inhibitory term, we reveal a threshold phenomenon in the phase space that governs the occurrence and non-occurrence of blow-up depending on the initial conditions and parameters. These results are established by reducing the system to a two-dimensional ODE via the linear chain trick, and analyzing the dynamics at infinity using Poincaré-type compactification, blow-up techniques, and the center manifold theorem.
