Delay differential equations have a wide range of applications in engineering. This work is devoted to the analysis of delay Duffing equation, which plays a crucial role in modeling performance on demand Micro Electro Mechanical Systems (MEMS). We start with the stability analysis of a linear delay model. We also show that in certain cases the delay model can be efficiently approximated with a much simpler model without delay. We proceed with the analysis of a non-linear Duffing equation. This model is a significantly more complex mathematical model. For instance, the existence of a periodic solution for this equation is a highly nontrivial question, which was established by Struwe. The main result of this work is to establish the existence of a periodic solution to delay Duffing equation. The paper claimed to establish the existence of such solutions, however their argument is wrong. In this work we establish the existence of a periodic solution under the assumption that the delay is sufficiently small.
Identifer | oai:union.ndltd.org:vcu.edu/oai:scholarscompass.vcu.edu:etd-6755 |
Date | 01 January 2018 |
Creators | Ospanov, Asset |
Publisher | VCU Scholars Compass |
Source Sets | Virginia Commonwealth University |
Detected Language | English |
Type | text |
Format | application/pdf |
Source | Theses and Dissertations |
Rights | © The Author |
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