The Exponential Stability of the Nerve Axon Equations
碩士 === 國立臺灣大學 === 數學研究所 === 98 === In this article, we survey the exponential stability of the nerve axon equations form Evans [3, 4], Sleeman [6], and Green and Sleeman [5]. In Section 1, we survey the stability of solution to the general system given by FitzHugh. Under small perturbations of a sol...
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| Format: | Others |
| Language: | en_US |
| Published: |
2010
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| Online Access: | http://ndltd.ncl.edu.tw/handle/11145220344540009065 |
| Summary: | 碩士 === 國立臺灣大學 === 數學研究所 === 98 === In this article, we survey the exponential stability of the nerve axon equations form Evans [3, 4], Sleeman [6], and Green and Sleeman [5].
In Section 1, we survey the stability of solution to the general system given by FitzHugh. Under small perturbations of a solution , the system can be characterized by the stability properties of the corresponding linearized system.
In Section 2, we explore the relation of the stability of the linearized system and the Fourier transform system. One can achieve a characterization of the stability at rest in terms of properties of the matrix [c d;e A].
The proof of the exponential stability of FitzHugh''s system and the characterization of the wave speed of the travelling wave solutions are put in Section 3.
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