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Abstract: The renormalization method which is a type of perturbation method is extendedto a tool to study weakly nonlinear time-delay systems. For systems withorder-one delay, we show that the renormalization method leads to reducedsystems without delay. For systems with order-one and large-delay, we proposean extended renormalization method which leads to reduced systems with delay.In some examples, the validities of our perturbative results are confirmedanalytically and numerically. We also compare our reduced equations withreduced ones obtained by another perturbation method.



Author: Shin-itiro Goto

Source: https://arxiv.org/







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