Renormalization Reductions for Systems with Delay

Details Renormalization Reductions for Systems with Delay Renormalization Reductions for Systems with Delay

2007-06-15

arxiv.org/abs/0706.2238v1

Nonlinear Sciences

Pattern Formation and Solitons

Submitted to Prog. Theor. Phys., 2 figures

Scientific paper

10.1143/PTP.118.211

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

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