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Algorithm for Rigorous Integration of Delay Differential Equations and the Computer-Assisted Proof of Periodic Orbits in the Mackey–Glass Equation
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نویسنده
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Robert Szczelina ,Piotr Zgliczyński
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منبع
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foundations of computational mathematics - 2018 - دوره : 18 - شماره : 6 - صفحه:1299 -1332
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چکیده
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we present an algorithm for the rigorous integration of delay differential equations (ddes) of the form (x'(t)=f(x(t-tau ),x(t))). as an application, we give a computer-assisted proof of the existence of two attracting periodic orbits (before and after the first period-doubling bifurcation) in the mackey–glass equation.
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کلیدواژه
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Computer-assisted proofs ,Delay differential equations ,Periodic orbit ,Topological methods ,Interval arithmetic 34K13 ,65G30 ,65Q20
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آدرس
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Jagiellonian University, Poland, Jagiellonian University, Poland
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Authors
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