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1、滯時(shí)微分動(dòng)力系統(tǒng)在神經(jīng)網(wǎng)絡(luò)、光學(xué)、生態(tài)學(xué)、自動(dòng)控制等許多領(lǐng)域具有廣泛的應(yīng)用。滯時(shí)微分動(dòng)力系統(tǒng)的特點(diǎn)是，當(dāng)前狀態(tài)的變化率不僅依賴(lài)于當(dāng)時(shí)的狀態(tài)，而且依賴(lài)于過(guò)去一段時(shí)間的狀態(tài)。近20年來(lái)，在滯時(shí)微分動(dòng)力系統(tǒng)解的基本理論、穩(wěn)定性理論、收斂性理論、分歧理論等許多方面都出現(xiàn)了重要的成果。 本論文主要研究求解滯時(shí)微分方程長(zhǎng)時(shí)間收斂的數(shù)值方法。首先，我們構(gòu)造了基于修正的Laguerre-Radau插值多項(xiàng)式的擬譜方法，建立了該數(shù)值方法的全局收斂
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