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• W2149608964 abstract "In this paper, the equivalence of the multiple time scales (MTS) method and the center manifold reduction (CMR) method is proved for computing the normal forms of ordinary differential equations and delay differential equations. The delay equations considered include general delay differential equations (DDE), neutral functional differential equations (NFDE) (or neutral delay differential equations (NDDE)), and partial functional differential equations (PFDE). The delays involved in these equations can be discrete or distributed. Particular attention is focused on dynamics associated with the semisimple singularity, and both the MTS and CMR methods are applied to compute the normal forms near the semisimple singular point. For the ordinary differential equations (ODE), we show that the two methods are equivalent up to any order in computing the normal forms; while for the differential equations with delays, we obtain the conditions under which the normal forms, derived by using the MTS and CMR methods, are identical up to third order. Different types of practical examples with delays are presented to demonstrate the application of the theoretical results, associated with Hopf, Hopf-zero and double-Hopf singularities." @default.
• W2149608964 created "2016-06-24" @default.
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• W2149608964 date "2014-01-01" @default.
• W2149608964 modified "2023-10-18" @default.
• W2149608964 title "Equivalence of the MTS Method and CMR Method for Differential Equations Associated with Semisimple Singularity" @default.
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• W2149608964 doi "https://doi.org/10.1142/s0218127414500035" @default.
• W2149608964 hasPublicationYear "2014" @default.
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