Multistate Stability of Synchronous Equations in Hindmarsh-Rose Networks
碩士 === 國立交通大學 === 應用數學系所 === 102 === In this thesis, geometric singular perturbation theory is applied to investigate multistate stability of synchronous equations derived from Hindmarsh-Rose Networks. Our main results contain the following. First, explanation of multistability of the synchronous Hi...
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2014
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| Online Access: | http://ndltd.ncl.edu.tw/handle/06760210703743412975 |
| Summary: | 碩士 === 國立交通大學 === 應用數學系所 === 102 === In this thesis, geometric singular perturbation theory is applied to investigate multistate stability of synchronous equations derived from Hindmarsh-Rose Networks. Our main results contain the following. First, explanation of multistability of the synchronous Hindmarsh-Rose equation can be given. For instance, we are able to conclude among other things that a bursting solution and a periodic solution with canard explosion can coexistence. The transition from initial states toward stable states can be fully predicted. Finally, the attraction region with respect to each stable state can be identified. This illustrates the power of using singular perturbation theory to understand the global dynamical properties of realistic biological systems.
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