此篇論文，我們考慮帶有非線性交互作用以及微小的擴散運動 此篇論文，我們考慮帶有非線性交互作用以及微小的擴散運動 此篇論文，我們考慮帶有非線性交互作用以及微小的擴散運動 此篇論文，我們考慮帶有非線性交互作用以及微小的擴散運動 此篇論文，我們考慮帶有非線性交互作用以及微小的擴散運動 此篇論文，我們考慮帶有非線性交互作用以及微小的擴散運動 此篇論文，我們考慮帶有非線性交互作用以及微小的擴散運動 此篇論文，我們考慮帶有非線性交互作用以及微小的擴散運動 此篇論文，我們考慮帶有非線性交互作用以及微小的擴散運動 此篇論文，我們考慮帶有非線性交互作用以及微小的擴散運動 的 廣義微生物趨向性模型。我們利用奇異擾動法來證明此系統的 廣義微生物趨向性模型。我們利用奇異擾動法來證明此系統的 廣義微生物趨向性模型。我們利用奇異擾動法來證明此系統的 廣義微生物趨向性模型。我們利用奇異擾動法來證明此系統的 廣義微生物趨向性模型。我們利用奇異擾動法來證明此系統的 廣義微生物趨向性模型。我們利用奇異擾動法來證明此系統的 廣義微生物趨向性模型。我們利用奇異擾動法來證明此系統的 廣義微生物趨向性模型。我們利用奇異擾動法來證明此系統的 廣義微生物趨向性模型。我們利用奇異擾動法來證明此系統的 廣義微生物趨向性模型。我們利用奇異擾動法來證明此系統的 廣義微生物趨向性模型。我們利用奇異擾動法來證明此系統行波解的存在性，我們也用到了動態系統中龐加萊理論。不考 行波解的存在性，我們也用到了動態系統中龐加萊理論。不考 行波解的存在性，我們也用到了動態系統中龐加萊理論。不考 行波解的存在性，我們也用到了動態系統中龐加萊理論。不考 行波解的存在性，我們也用到了動態系統中龐加萊理論。不考 行波解的存在性，我們也用到了動態系統中龐加萊理論。不考 行波解的存在性，我們也用到了動態系統中龐加萊理論。不考 行波解的存在性，我們也用到了動態系統中龐加萊理論。不考 行波解的存在性，我們也用到了動態系統中龐加萊理論。不考 行波解的存在性，我們也用到了動態系統中龐加萊理論。不考 行波解的存在性，我們也用到了動態系統中龐加萊理論。不考 慮微生物有擴散運動的時候 慮微生物有擴散運動的時候 慮微生物有擴散運動的時候 慮微生物有擴散運動的時候 ，我們透過分析其對應的代數微系統 ，我們透過分析其對應的代數微系統 ，我們透過分析其對應的代數微系統 ，我們透過分析其對應的代數微系統 ，我們透過分析其對應的代數微系統 ，我們透過分析其對應的代數微系統 ，我們透過分析其對應的代數微系統 給出 了脈衝解的存在性必要條件。 脈衝解的存在性必要條件。 脈衝解的存在性必要條件。 脈衝解的存在性必要條件。 脈衝解的存在性必要條件。 脈衝解的存在性必要條件。 在奇異擾動法的理論保證之 奇異擾動法的理論保證之 奇異擾動法的理論保證之 奇異擾動法的理論保證之 下， 此必要條件一樣適用於當微生物有小的擴散運動形況。同 此必要條件一樣適用於當微生物有小的擴散運動形況。同 此必要條件一樣適用於當微生物有小的擴散運動形況。同 此必要條件一樣適用於當微生物有小的擴散運動形況。同 此必要條件一樣適用於當微生物有小的擴散運動形況。同 此必要條件一樣適用於當微生物有小的擴散運動形況。同 此必要條件一樣適用於當微生物有小的擴散運動形況。同 此必要條件一樣適用於當微生物有小的擴散運動形況。同 此必要條件一樣適用於當微生物有小的擴散運動形況。同 此必要條件一樣適用於當微生物有小的擴散運動形況。同 此必要條件一樣適用於當微生物有小的擴散運動形況。同 時我們藉由譜分析 時我們藉由譜分析 時我們藉由譜分析 來討論利用上述奇異擾動法找出的脈衝解線 來討論利用上述奇異擾動法找出的脈衝解線 來討論利用上述奇異擾動法找出的脈衝解線 來討論利用上述奇異擾動法找出的脈衝解線 來討論利用上述奇異擾動法找出的脈衝解線 來討論利用上述奇異擾動法找出的脈衝解線 來討論利用上述奇異擾動法找出的脈衝解線 來討論利用上述奇異擾動法找出的脈衝解線 性穩定。 性穩定。

In this paper, we consider a generalized model of 2  2 Keller-Segel system with
nonlinear chemical gradient and small cell diusion. The existence of the traveling pulses
for such equations is established by the methods of geometric singular perturbation (GSP
in short) and trapping regions from dynamical systems theory. By the technique of GSP,
we show that the necessary condition for the existence of traveling pulses is that their
limiting proles with vanishing diusion can only consist of the slow
ows on the critical
manifold of the corresponding algebraic-dierential system. We also consider the linear
stability of these pulses by the spectral analysis of the linearized operators.

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